"Yes, McGeady was suspended from training with the first team for not complying with my instructions in training and matches," the Russia international Karpin told reporters. "The rest is our internal affair."
Local media reported McGeady, capped 63 times by Ireland, has been criticised by Karpin for poor form and his performance in Spartak's 1-0 loss to city rivals CSKA last Saturday.
Several Russian newspapers said the 27-year-old winger would be allowed to play only in Spartak's reserve team and would leave the club in January.
"All of us were surprised to see the Irishman on the field and asked him what happened," a reserve team's player told Izvestya newspaper on condition of anonymity after Friday's training session.
McGeady joined Spartak from Celtic in 2010 on a four-and-a-half-year contract for a reported fee of around 9.5 million pounds ($15.53 million).
Spartak, who are third in the standings with 33 points from 17 matches, three points behind leaders Zenit St Petersburg, take on Volga on Sunday.
($1 = 0.6118 British pounds)
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