Blue Jackets general manager and president Doug MacLean said he will come up with a list of candidates to fill the job permanently and present it to the team's owners.
No timetable has been set.
"Gary is an excellent coach who knows our players well and we're confident he'll do an outstanding job," MacLean said in a release. "At the same time, it is our responsibility to re-evaluate our personnel and organizational needs to ensure the long-term success of our hockey club. That process will begin immediately."
Gallant was fired after one full season and parts of two others.
The Blue Jackets, a team with lots of young talent who many considered ready to contend for their first playoff spot, are off to a 5-9-1-0 record that leaves them in last place in the Western Conference's Central Division.
They host Nashville on Wednesday.
"A lot of hockey remains to be played this season," MacLean said. "Despite our disappointing start, we remain committed to building a team that will be successful on the ice."
Agnew is in his first year with the Blue Jackets after coaching the club's American Hockey League in Syracuse the previous six seasons.
He led the Crunch to a 200-177-43-40 record in 480 games and left as the winningest coach in franchise history.
Before joining the Crunch, Agnew spent 10 seasons as a head coach in the Ontario Hockey League, the final three with the London Knights.