Edmonton tapped Paajarvi earlier in the day, but was informed by the NHL that he was an ineligible roster selection.
"We believed we had confirmation to recall Magnus as one of our four call-ups after the trade deadline," said Oilers general manager Steve Tambellini in a statement. "The league informed us today the only way he could be recalled was under an emergency recall basis."
The 20-year-old has two goals and six assists with Edmonton in 41 games this season to go along with 22 points (five goals, 17 assists) in 27 games with the Barons.
The six-foot-two 204-pound Swede played 80 games with the Oilers in 2010-11, collecting 15 goals and 19 assists.
The Oilers announced earlier this week that forward Taylor Hall will miss the rest of the season because of shoulder surgery.
Edmonton has been eliminated from playoff contention but hosts the Los Angeles Kings on Friday in a key encounter in the tight Western Conference post-season chase.
The Kings sit eighth in the conference but are tied with ninth-place San Jose on points with 88.