"We have lost two important players for at least three weeks so it is important now not to lose any more," said Arsenal manager Arsene Wenger on Sunday.
Arsenal beat Bolton 2-0 to move within three points of leaders Chelsea.
Frenchman Nasri, 22, has played 14 times for the Gunners this season, scoring three times, while 18-year-old Ramsey has four goals from 24 appearances.
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"Nasri was injured in the final minute of training and he has a hamstring strain and Aaron Ramsey has a thigh problem," added Wenger.
"The injury is high up on his thigh but I think it is short term."
Three weeks out would see the pair miss league games against Bolton, Aston Villa, Manchester United and Chelsea, as well as the FA Cup fourth round tie at Stoke.
Arsenal are fighting on three fronts - Premier League, FA Cup and Champions League - and Wenger's squad is being tested to the full.
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The Frenchman is already without forwards Theo Walcott (rib), Nicklas Bendtner (hernia) and Robin Van Persie (ankle) while midfielders Denilson (rib) and Jack Wilshere (hamstring) are also missing.
But Wenger was able to recall Cesc Fabregas for Sunday's victory with the Spain midfielder scoring in his side's win.
Defender Gael Clichy was also on the bench having missed several months with a back problem.
"I am very short in midfield at the moment so even I am trying to practise at the moment," added Wenger.
Source: BBC Sport
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