There has been bad blood between the pair since Frimpong reacted to Nasri's £24million switch to City in August by tweeting: "Money is the root of all evil."
And the pair squared up to each other after Sergio Aguero's 83rd-minute winner booked City's place in the last four of the Carling Cup.
A Gunners spokesman said: "Words were exchanged — and that was that.
"No punches were thrown but there was a lot of noise. Samir was speaking in French but they did not touch. It was handbags."