The club has been demoted from the Championship.
Oakwell has had two head coaches leave this season, the other being Markus Schopp.
The Tykes have lost six of their 43 league games and have been demoted.
The final three games of the campaign will be taken over by Martin Devaney.
The 41-year-old, who will be assisted by Tom Harban and Jo Laumann, was a member of the Barnsley side that won promotion from League One in 2006 and reached the FA Cup semi-finals two years later.
Schopp was replaced by Asbaghi after a run of only one win in 15 games.
Asbaghi won only five of his 36 matches in charge.
I would like to thank everyone at Oakwell for their time and efforts over the last few months. The 36-year-old said that this includes players, fans and staff.
It has been a pleasure to work in Barnsley and I wish everyone the best for the upcoming season.
The assistant to Asbaghi has left the club.
Since February of last year, the seventh boss has been left by Paul Heckingbottom.
The search for a new coach has begun and an announcement will be made once the process is concluded, said chief executive Khaled El-Ahmad.
Nancy, who have the same owners as Barnsley, were also demoted on Friday evening.
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