Assistant coach Markku Kanerva will replace the 64-year-old Swede on a three-year contract with Finland lying fifth in 2018 World Cup qualifying Group I on one point from four games.
"We had a lot of misfortune, an unforeseen amount of injuries and absences. Still, top-level football is a result sport and these results did not satisfy anybody," Finnish FA chairman Pertti Alaja said in a statement.
One of the team's key players, midfielder Roman Eremenko, has been suspended since October after testing positive for cocaine.
Backe, previously coach of FC Copenhagen and New York Red Bulls, was criticised in Finland for playing with a five-man defence which reduced the team's attacking threat.
Finland, ranked 93rd in the world, have never qualified for the finals of the World Cup or European Championship.
(Reporting by Jussi Rosendahl, editing by Ed Osmond)
