The central defender is reported to have been trying to sell his five tickets at £200 apiece.
A club spokesman said: "The club is saddened that Nathan has been so foolish.
"All of the players were made aware that tickets for the Carling Cup final are available for their own use only and, following this incident, the message has been repeated to them.
"Nathan's actions were naive and he is extremely embarrassed and regretful at having let himself down at the club and the Aston Villa fans.
"It shouldn't be forgotten, however, that Nathan is just 18 years old and he has a lot to learn."
Baker is regarded as one of Villa's most exciting young talents for the future although he has yet to make a senior appearance for Martin O'Neill's side and is currently on loan at League Two side Lincoln.
Carling Cup 2009/10 Win Outright: Aston Villa 7/4