All passengers have been evacuated to land with no injuries, the company reported.
The ship was on the Turku–Stockholm route when the grounding occurred at 1250 local time. The extent of damage is being investigated.
The ship will be replaced on Monday by the MS Gabriella until further notice, the company said.
The MS Amorella was built in 1988 and has capacity for 2,480 passengers and 450 cars. It runs daily voyages from Turku to the Stadsgården terminal in Stockholm, according to Viking Line’s website.
The cause of the grounding was not immediately clear.
AIS ship tracking from MarineTraffic.com shows the voyage of the Amorella: