Stroll was one of a handful of drivers to stay out on slick tyres as the rain fell at the Sochi Autodrom.
The Canadian hit the back of Gasly when recovering from a spin of his own.
It was one of two incidents that Stroll was involved in late on, colliding with Aston Martin teammate Sebastian Vettel a few laps earlier.
Stroll’s 10-second penalty has no impact on his race result, leaving him in 11th, but the two additional penalty points bring his total up to eight – 12 results in a race ban.
The stewards deemed that Stroll was “wholly to blame” for the collision with Gasly which occurred at Turn 8.
“Although noting the evidence of the driver of car 18 [Stroll] that the conditions were extremely slippery especially as he was on old hard tyres, the stewards determined that it was still the responsibility of the driver to ensure that having left the track due to those very same conditions, he drove appropriately taking them into account when he rejoined and turned into the next corner, considering there were two other cars in close proximity,” the stewards noted.
Three penalty points will expire on Stroll’s license the day after the United States Grand Prix next month.
Giving his view on the incident, Gasly said: “I think he went in the wall, came back, turn 8 clipped my wheel, I haven’t seen the footage but I just turned and he touched me and basically I spun the car.”