Dubinsky had a goal and an assist Saturday in a 3-1 win over the Preds.
Dubinsky had a solid first season with Columbus and can get ready for 2013-14.
Dubinsky returned Friday for the Jackets.
Dubinsky was out with an illness.
Dubinsky had two assists in his return from a lower-body injury Thursday, a 3-1 win over Nashville.
Dubinsky, who has 11 points this season, had missed six straight games.
Dubinsky has been placed on injured reserve with a left knee injury.
It is unclear when Dubinky will be healthy enough to return.
Dubinsky had a goal and an assist and the Blue Jackets dominated against the NHL's stingiest defense in a 6-2 victory over the San Jose Sharks on Monday night.
Dubinsky is tied for second on the team with seven points.
Blue Jackets forward Dubinsky was fined $10,000 Wednesday, the maximum allowed under the new NHL collective bargaining agreement, for boarding Los Angeles defenseman Rob Scuderi in Columbus' 4-2 loss to the Kings on Tuesday. He will not be suspended.
The incident occurred at 11:29 of the second period, and set off a rash of penalties. Not long after, Dubinsky and Los Angeles forward Mike Richards fought. All told, 37 minutes in penalties were handed out, and Dubinsky was assessed a major penalty for the original incident, as well as a game misconduct.
Dubinsky has been traded along with Artem Anisimov, defenseman Tim Erixon and a first-round pick next year to Columbus for Rick Nash.
Dubinsky immediately becomes one of the top forwards for a floundering Columbus franchise.