Hart was City's bloodied hero in Saturday's 1-0 win over Crystal Palace, playing on with a wound just below his left eye after a collision with Cameron Jerome.
But Pellegrini expects to name the reinvigorated England international in goal at the Liberty Stadium in Wednesday's fixture, which is live on Sky Sports 1HD.
"Joe Hart has a cut beneath his eye but it's not dangerous and he can play without risk," the Chilean said at Monday's pre-match press conference.
Hart's string of key saves against Palace, following a standout display in the Boxing Day victory over Liverpool, was further evidence of his return to form after a troubled few months.
The 26-year-old was dropped for seven Premier League games after a series of mistakes that culminated with an error that allowed Chelsea's Fernando Torres to score the winner at Stamford Bridge in October.
"Everyone knows why Joe Hart is the first choice goalkeeper here," Pellegrini added.
"He's played for two or three years at a very high (level of) performance; he can do it so we hope that he will continue in the same way."
City travel to Swansea just a point behind leaders Arsenal and Pellegrini admitted his delight at a month that has seen them make up valuable ground.
"It was a fantastic month for us: we played 10 games and we won nine and drew one," Pellegrini said.
"In the Premier League we won six of the last seven so we have recovered points. Arsenal were six points ahead of us. It's very important to finish the year in this position. We would have liked to have been first but we have recovered points.
"In the first six months we have prepared for all the competitions we have been in and now, in the second half, we try to win."
Watch Swansea v Manchester City live only on Sky Sports 1 HD from 12.30pm on New Year's Day.