Ramsey enjoyed a superb first half of the campaign, scoring 13 goals, but has not featured since coming off at West Ham on Boxing Day because of a thigh problem.
Wenger confirmed after Tuesday night's frustrating 2-2 home draw against Swansea, where the Gunners conceded a last-minute own goal from Mathieu Flamini, Ramsey had suffered a "little setback" in his rehabilitation.
Saturday's visit of Barclays Premier League title challengers Manchester City had been pencilled in for a return, but Wenger confirmed to the club's official website on Thursday there would be no quick recovery for the dynamic Welshman.
"Compared to Tuesday night, we have no new injuries and no-one coming back as well," said Wenger, who is also without the likes of Jack Wilshere and club-record signing Mesut Ozil.
"(Nacho) Monreal should be the first one back in training because he is just starting to run in the next few days. After him, Ramsey is progressing well, but we need to be patient for a few more weeks."
Arsenal tackle a rampant City side in need of a performance following the disappointing ending to Tuesday night's match, which for a spell had seemed set to draw a line under the 6-0 humiliation at Chelsea which ruined Wenger's 1,000th match in charge.
The Gunners boss, however, accepts there is little option other than to look to regroup once more in spite of all the questions which have again been left unanswered.
"We have to do that (restore belief) as well as we can and accept our position at the end of the season, but at the moment [our focus] is to recover from a high disappointment and recover for the next game. It is a huge game," said Wenger.
Arsenal have yet to announce any firm decision on Wenger's own future, or indeed that of full-back Bacary Sagna, who is out of contract in the summer and is reportedly attracting interest from both Manchester City and Inter Milan after the veteran France international was said to have rejected a two-year extension.
Wenger, though, appears to be already laying plans for next season, with the announcement of a friendly in New York during July.
Arsenal will take on Major League Soccer outfit New York Red Bulls at the Red Bull Arena, where they will face off against former captain and club record goalscorer Thierry Henry.
Wenger said: "This will be a great chance to play in front of supporters who have not seen the team play before.
"The New York Red Bulls will be midway through their season, so they will provide a good test.
"Obviously it will be good to play against Thierry. He is a very special player in our club's history and I know the players and the supporters will enjoy this very much."
Henry added in a statement on Arsenal's website: "It goes without saying that hosting Arsenal at Red Bull Arena will be a special moment for me both on a professional and personal level.
"As I have said before, the club is in my heart and this will be another terrific chapter in my relationship with Arsenal Football Club.
"Along with my team-mates, I am excited to host Arsenal in New York - one of the greatest cities in the world - and hope that Red Bulls and Arsenal fans will be able to enjoy the match."