Tournament officials announced the outcome following a disciplinary hearing in Dublin.
Estebanez, who pleaded not guilty after being cited for the offence, cannot play again until February 11 and will miss Racing's Heineken clash against Munster in Limerick on Sunday.
Strettle was carried off following the third-minute incident in Nantes, although he has now recovered and is in selection contention for Saracens' final group game against Edinburgh on Sunday.
Independent judicial officer Pat Barriscale heard evidence and submissions from Estebanez.
In a statement, European Rugby Cup said: "The judicial officer upheld the complaint and found that Estebanez had committed a reckless act.
"He determined that the act was in the mid range (five weeks) of the IRB (International Rugby Board)'s sanctioning regime, and taking into account the limited mitigating factors of the player's remorse and good conduct during the hearing, the judicial officer reduced the suspension by one week."
Stade Francais player Juan Cruz Guillemain, who also appeared at a Dublin hearing, was banned for five weeks.
Guillemain was cited for striking Grenoble player Fabien Alexandre with his head during last Saturday's Amlin Challenge Cup game between the clubs. Guillemain can play again on February 18.