Parssinen was scratched for the eighth time in 11 games when he sat out Saturday's 5-2 loss to the Avalanche.
Parssinen notched an assist and four hits in Monday's 3-2 overtime loss to the Avalanche.
Parssinen scored a goal in Thursday's 6-2 loss to the Panthers.
Parssinen scored his first goal of the season in Wednesday's 3-2 loss to the Capitals.
Parssinen was assigned to AHL Milwaukee on Monday.
Parssinen agreed to terms on a one-year $775,000 contract with Nashville on Monday.
Parssinen was reassigned to AHL Milwaukee on Saturday.
Parssinen was called up from the AHL on Thursday, per Robby Stanley of NHL.com.
Parssinen was loaned to AHL Milwaukee on Tuesday.
Parssinen produced a goal and an assist in Friday's 6-5 overtime win over the Hurricanes.