Premier League: Arsenal at the double for monthly awards
Arsenal won four successive Premier League games in March, scoring nine goals and conceding two.
France international Giroud scored five times, with a brace at Newcastle adding to goals against Everton, QPR and West Ham.
It is the 14th time Wenger, 65, has won the award in 19 years at Arsenal.
Arsenal are third in the Premier League table with eight matches remaining. They are seven points behind leaders Chelsea, who have a game in hand.
The Gunners host fifth-placed Liverpool at The Emirates on Saturday.
Arsenal's remaining games also include a home match against Chelsea on 26 April and a trip to fourth-placed Manchester United on 17 May.