"I am OK. Thanks to everyone who has shown their concern," Shockey said in a message posted on his Twitter account. "Don't worry about me. I will be fine."
Saints safety Darren Sharper, who was seen at the hospital where Shockey was being treated, also was with Shockey in the Saints' weight room when the seizure took place.
"It was scary," Sharper said. "We didn't know what was going on."
Sharper said trainers quickly attended to the star tight end, who seemed lucid again after about a minute and was able to walk on his own to an ambulance.
"He said he just felt light-headed," Sharper recalled.
One player told NewOrleans.com that Shockey was shaking and "he was basically out of it for probably a minute or so, but it seemed longer." The player said Shockey seemed aware after that and was walking around when he left for the hospital.
NewOrleans.com and ABC26 television first reported the incident.
It was not immediately clear how long Shockey would be hospitalized.
Last summer, before the 2009 training camp began, Shockey had to be hospitalized after passing out from dehydration at a party in Las Vegas.
Shockey had just completed three straight days of offseason training sessions at team headquarters before Thursday's seizure occurred.
The Saints did not officially comment on Shockey's condition, leaving unclear his prospects for getting back on the field when the Saints return to their suburban New Orleans headquarters for minicamp June 4-6.
Shockey was instrumental in helping the Saints win their first Super Bowl last season. He had 48 catches for 569 yards and three touchdowns during the regular season, then in the playoffs had seven catches for 58 yards and two TDs. His final score put the Saints ahead for good in the fourth quarter of their Super Bowl win over the Indianapolis Colts.
Also at the Saints' OTA, the team said that cornerback Malcolm Jenkins is working out at free safety.
"We'll move him around," said Saints head coach Sean Payton. "He's working at free. He's a guy that has good versatility. He can come down and play in the box. He can play in the safety position, in the nickel packages. Gregg [Williams, the team's defensive coordinator] and those guys will do a great job of utilizing his skill set, but he's doing well and working primarily at free safety."
Information from The Associated Press and ESPN NFL Insider Adam Schefter is included in this report.