Bjorn reacted angrily Monday after Woosnam overlooked him and selected Darren Clarke and Lee Westwood as his captain's picks. Ten other players made the team automatically for the Sept. 22-24 matches against the United States at The K Club outside Dublin.
Bjorn was fined by the European Tour for his comments.
'Having had a day to reflect on my comments, I would like to apologize for the hurtful and personal nature of my remarks to European captain Ian Woosnam,' Bjorn said.
'I realize I have made a mistake and, as such, have unreservedly apologized to Ian for my comments, which were made in the heat of the moment following the disappointment of not making it onto the European team.'
Bjorn said Woosnam had failed to communicate with the players. Woosnam notified Clarke before announcing his choices on Sunday, but did not tell Westwood or Bjorn beforehand of his choice.
'He's not taken charge of the captaincy in the way I see a captain should take charge and it's disappointing,' Bjorn said Monday. 'He never called me. He came into the bar at the hotel and gave me 20 seconds about Lee having won twice at The K Club. In a bar. That kind of sums it up.'
European Tour executive director George O'Grady said in a statement Tuesday that it had fined Bjorn for the comments.
'The European Tour will not tolerate comments such as the personal and unacceptable remarks made by Thomas on Ian Woosnam,' O'Grady said. 'We are aware that he has apologized to Ian Woosnam, and he has also apologized to the Tour.'