With midfielder Thiago Motta and forward Lucas also out, Ancelotti could hand David Beckham his first league start since he joined the French leaders in January on a five-month deal.
The former England captain, who started the French Cup last-16 win over Olympique Marseille, has featured in three league games so far as a substitute.
"We'll miss four players at St Etienne but the team will be competitive," Ancelotti told a news conference.
St Etienne, who are unbeaten in 2013, were the first Ligue 1 side to beat PSG this season. They also eliminated PSG on penalties in the League Cup.
"I think it's time for them to lose some games," Ancelotti said.
PSG top the table with 57 points from 28 games, four ahead of second-placed Olympique Lyon, while St Etienne, fourth with 48, can climb to third if they win on Sunday.
Verratti, the Italian midfielder, has a thigh muscle injury and Menez has a hamstring problem.
Menez will undergo further medical tests when he joins the France squad on Monday ahead of next Friday's World Cup qualifier at home to Georgia. Les Bleus then host Spain on March 26.