The Argentinian striker was given extra time to recover following his international duty at the Copa America earlier this summer.
The 27-year-old had been expected to return to training at City on Thursday ahead of their Community Shield match this weekend but will now resume training next week.
"I have spoken to him, his phone is working again," said City boss Mancini. "He was happy and told me he would come back on Monday - everything was normal.
"He was on holiday, there was a mistake. We said he needed to come back on August 5 with Zaba [Pablo Zableta] but it was my mistake because I told him to come back on August 8.
"Carlos comes back on Monday because he has 21 days after the Copa America."
Tevez has indicated that he wants to leave City, although a £40m move to Corinthians collapsed last month.