"This was a criminal act and highly reckless. It risks lethal retaliation and a new round of regional conflict," Brennan tweeted on Friday.
"Iranian leaders would be wise to wait for the return of responsible American leadership on the global stage and to resist the urge to respond against perceived culprits," he added.
Fakhrizadeh was assassinated by unknown gunmen in a small city east of Tehran on Friday evening.
After sustaining injuries from a car explosion and bullets, the top scientist was taken to the hospital with a helicopter but succumbed to injuries a few hours later.