Jesus had been struggling with fluid on the knee but recovered to play and score in Arsenal's 2-1 win over Nottingham Forest on Tuesday, before being replaced late in the second half.
Partey has had multiple injury problems this season, and hasn't played since October, with just four league appearances this campaign, but had returned to training last week and had been expected to make a return to the squad.
"Gabi (Jesus) played and trained with us the whole week," Arteta told a press conference.
"With Thomas, unfortunately, we had a little setback a few days ago. He's not going to be available in the squad. We don't know if it's a few days or weeks.
"He was getting some momentum at the start of the season and then we lost him for a while. Now we have been a long time without him."
After the win over Forest, Oleksandr Zinchenko and Ben White were involved in a heated argument as they left the pitch, over the late goal conceded, but Arteta laughed off the incident.
"They've been in the same house the past few days sharing wives and everything. They're living together now. They are best mates," the manager joked.
"You don't argue with someone if you don't have a great relationship. That happens because you have the trust and chemistry to react the way they did.
"I want to see passion, I want to see commitment from my players."
Arsenal go into Sunday's home game with Premier League leaders Liverpool in third place, level on points with Manchester City in second but five points off top spot.
A run of three games without a win in December, including a 1-1 draw at Anfield, saw them lose their place at the top, but the Gunners come into this game on the back of two consecutive victories.
"We talk about momentum and we won the last two games, I want to win the third one, especially at home with our people, it's going to be an incredible atmosphere and we're going to need that."
