Cobb was taken off the field on a stretcher after he was hit on the right ear by a liner off the bat of Kansas City's Eric Hosmer in the fifth inning of the Rays' 5-3 win over the Royals on Saturday.
Rays spokesman Rick Vaughn said all tests were normal and that Cobb suffered a mild concussion. Cobb was taken to Bayfront Medical Center in St. Petersburg, where he will spent the night.
Cobb put a hand on his head after being struck. Trainers from both teams and other medical staff immediately ran onto the field. Cobb could be seen kicking his legs while being examined on the mound.
The team said Cobb remained conscious the whole time.
Players on both teams had hands on their heads as a stunned silence overtook Tropicana Field after the crowd gasped when Cobb was struck. Rays head athletic trainer Ron Porterfield and Dr. Michael Reilly went with Cobb to the hospital.
Tampa Bay pitcher David Price visited Cobb in the hospital and tweeted: "Cobber is way more tough than me!! Laughing at jokes and the name they gave him!! Please keep him and his family in your prayers."
"He seemed pretty normal, so that was good," Price said after returning to the ballpark. "Our hearts are with him. He told me that Porterfield was making him really mad on the field because he wouldn't let him stand up, so it was good that he wanted to be able to stand up. He knew where he was. It's amazing that he is in the condition I feel like he is in right now."
Hosmer's drive bounced back toward the plate area, where catcher Jose Lobaton picked up the ball and threw him out at first.
"He hit it so hard (Cobb) couldn't even react, and it makes everybody in the stadium sick to their stomach when something like that happens," Royals manager Ned Yost said.
Hosmer said he didn't even want to run to first.
"I just wanted to see how he was doing," Hosmer said. "You hate to see that, especially Alex having a great year. It's just scary stuff, man. I'm glad he's alright. I know he's been talking and having conversations."
Hosmer, and Cobb's former teammates James Shields and Elliot Johnson planned to visit the pitcher at the hospital.
"I just want to go there and show him I care how he's doing," Hosmer said.
Cobb being hit came a month after Blue Jays starter J.A. Happ was also struck by a liner against the Rays and suffered a skull fracture. Happ was discharged from an area hospital the following day.
The sound of the ball striking Cobb -- which sounded like a bat hitting a ball -- could be heard in the press box and throughout the ballpark.
"I think everybody heard it," Rays right fielder Matt Joyce said. "The loudest and worst ball hitting somebody I've ever seen. Obviously the same happened with Happ here and that was terrifying, too. But man, that one caught him square."
Rays players, manager Joe Maddon and pitching coach Jim Hickey gathered at the mound during the 11-minute delay. Shortstop Yunel Escobar was in squatting position looking down at the ground, while Hickey appeared at time at be nervously pacing near the mound.
"When they rolled him over, Cobber was talking and that was a good thing," Maddon said. "It's one of those really, really bad moments. It's part of the game and it stinks sometimes. Just a horrible moment to witness. It doesn't happen often, thank God, but when it does it can really give you pause. We were very lucky. Of course Alex was very lucky."
"I thought our medical staff did a great job," Maddon added. "They were beyond professional with how they dealt with the entire moment."
It has been a tough week for Cobb, who left the team after starting Monday night's game against Boston due to the death of his grandmother. He was informed of the death after the game in which the 25-year old gave up a season-high six runs over four innings in a 10-8, 14-inning loss to the Red Sox.
"So everything's looking positive and from everything I've heard, he has a laceration on his ear and a concussion," Shields said. "Hopefully it's just that."
Luke Scott, Joyce and Evan Longoria homered for the Rays, who had lost five of six. Alex Torres (2-0) replaced Cobb and struck out four over 1 2-3 scoreless innings. Fernando Rodney pitched the ninth for his 14th save in 19 opportunities.
"I'm still shaking," Torres said.
Joyce hit a solo homer off Jeremy Guthrie (7-4) in the fifth that put the Rays up 4-2 and ended the Royals' 13-game stretch of limiting opponents to three runs or fewer.
"Such a heart-wrenching and terrible thing to happen on a baseball field, but at the same time you have to finish the game," Joyce said. "The only thing you can do is just pray that he's OK and pray for a speedy recovery."
Guthrie gave up five runs and eight hits over seven innings.
Scott hit his first homer since May 19, a two-run drive during the third as Tampa Bay grabbed a 3-2 lead. Scott, who had make all of his 29 previous starts this season at designated hitter, started in left field with third baseman Longoria moving into the DH role.
Longoria, bothered the past two weeks by plantar fasciitis in his right foot, was the DH for the third straight game. He made it 5-2 on a sixth-inning solo homer and also had a sacrifice fly in the first.
Longoria is expected to DH again Sunday and could play in the field when the Rays start a road trip Tuesday at Boston.
The Royals took a 2-1 lead in the second when Alex Gordon walked on a 3-2 pitch with the bases loaded and Hosmer hit a sacrifice fly. Salvador Perez cut the deficit to 5-3 on a solo homer in the eighth.
Perez extended his hitting streak to 11 games with a single in the first.