Monday's 3-0 loss away to Sevilla left the Andalusians just two points above the bottom three ahead of a daunting run of fixtures that includes meetings with Real Madrid and Barcelona in the next three matches.
"The board of Granada CF has...removed the coach Juan Antonio Anquela," said a statement on the club's website.
"The club is now working to hire a new coach. Granada CF thank Anquela for his involvement and work and wish him every success in his future career."
Anquela joined Granada in the summer after guiding Alcorcon into the Segunda Division.
The side had finished 17th in the table last year under Abel Resino in their first season following promotion.