The 23-year-old had 14 assists in 53 NHL games last season, both career highs.
The Eksjo, Sweden native was a key piece sent to Ottawa in the Mark Stone trade with the Vegas Golden Knights in 2019.
"Erik is among our group of young players who we’re looking upon to take another step forward next season," said Senators general manager Pierre Dorion in a statement. "He’s competitive, has an ability to efficiently move the puck and showed well when asked to take on an increased role last season. We’re hopeful that experience pays dividends for him in the year ahead."