The Argentinian left the field in the 76th minute after scoring a hat-trick during Manchester City's 5-0 FA Cup victory at the Etihad Stadium.
The Citizens are now in the last four of the competition for the second time in three years.
And Platt, City's assistant manager, said: "His hamstrings just tightened up at the end, which is why we took him off.
"Hopefully, with a couple of days rest he will be back again and ready for next week."
Sergio Aguero is currently sidelined with a knee injury, so City cannot afford to take any chances.
Tevez, meanwhile, has now moved on to 15 goals for the season having found the net in his last four matches - after scoring just once in his previous 11.
Platt added: "Carlos has got better as the season has gone on.
"He had a little patch where he didn't score goals but he has had efforts on goal and was full value for this hat-trick."