The Gunners started the new Premier League campaign at Liverpool on Sunday with an already depleted squad but managed to salvage a point following a stoppage-time own goal by Reds goalkeeper Jose Reina.
However, Arsene Wenger must also now do without the versatile Nasri - who often came inside to cover for captain Cesc Fabregas in central midfield - for probably the next five games, which also include the start of the Champions League campaign in mid-September.
A club statement read: "Arsenal midfielder Samir Nasri will today undergo minor surgery on his knee following a meniscal injury sustained during the match against Liverpool on Sunday.
"Nasri, who has been in impressive form, will be out of action for a month."
Fabregas missed the trip to Anfield because of illness, but the World Cup winner - now fully focused on Arsenal after a much-hyped, big-money summer move to Barcelona failed to materialise - is expected to be back in contention for the visit of new boys Blackpool to the Emirates Stadium on Saturday.
However, with Alex Song hampered by a calf injury which kept the Cameroon midfielder on the bench at Liverpool, Denilson not making the trip to Merseyside at all because of an abdominal problem and Wales international Aaron Ramsey still some way
from a return after his broken leg last season, England teenager Jack Wilshere could be in line for only his second Premier League start against the Tangerines.
Wenger, though, has more worries in the centre of defence.
Summer signing Laurent Koscielny will serve a suspension after his sending-off for two late yellow cards at Anfield. If Johan Djourou, just back from a long-term knee injury, fails to makes a quick recovery from his hamstring problem, then Song could be asked to partner Thomas Vermaelen at the heart of the Gunners' back line.
The Gunners boss, meanwhile, must also make a decision on his goalkeeper.
Manuel Almunia, whose position as number one has come under the spotlight, captained the side at Liverpool, but the Spaniard admits he would consider his future were the Gunners to sign experienced competition such as wantaway Fulham stopper Mark Schwarzer or possibly Shay Given. The Republic of Ireland international may be looking for a move after Roberto Mancini appeared to place Joe Hart above him in the Manchester City pecking order.