A spokesman for the singer said she will be canceling an appearance in Istanbul on Monday and in Athens on Wednesday.
The spokesman said Sunday that Winehouse would like to extend her apologies to fans expecting to see her, but "feels that this is the right thing to do."
He added that she will return home after agreeing with management that "she cannot perform to the best of her ability."
The singer, who has publicly struggled with drugs and alcohol, was jeered late Saturday as she performed in Serbia's capital Belgrade. She stumbled onto the stage, mumbled through her songs and sometimes wandered off.
The Associated Press contributed to this report.