The 35-year-old suffered the injury in Saturday's 2-2 draw at Swansea when despite finishing the game, he left the stadium on crutches.
Terry will now miss his side's Premier League clash with Liverpool on Friday as well as next week's League Cup trip to Leicester.
In a post on his Instagram account, Terry wrote: "I have strained my ligaments in my ankle which means I will be out for 10 days.
"Absolutely gutted, but will be giving everything to get back playing."
Terry's diagnosis may not be as bad as was first feared but will still provide boss Antonio Conte with a defensive headache ahead of the Liverpool game.
Conte was unimpressed by some of his side's defending at the Liberty Stadium, although Terry escaped culpability for either of the Swansea goals.
Returning Brazilian David Luiz, who was on the bench at Swansea, is most likely to replace Terry for the clash with Jurgen Klopp's men.
The Chelsea statement read: "John Terry's injury suffered in Sunday's game at Swansea is strained ligaments in his foot
He will be out for approximately 10 days.
"Our captain was injured in the closing minutes of the 2-2 draw at the Liberty Stadium
He completed the game in pain and Antonio Conte confirmed afterwards the problem would need medical assessment."
Source : PA
Source: PA