Dijkhuizen's assistant, Roy Hendriksen, has also left the Championship club.
Brentford won only two of their eight league games under the Dutchman, 43, and are 19th in the table.
Former Blackburn, Coventry and Everton midfielder Carsley, 41, had been working as manager of Brentford's development squad.
Media playback is not supported on this device
Dijkhuizen was appointed head coach by Brentford in June, following the controversial departure of previous boss Mark Warburton.
It was confirmed in February that Warburton, who went on to lead the Bees into last season's play-offs, would leave the club at the end of the campaign.
Warburton had guided Brentford to promotion from League One the previous season.
A former striker, Dijkhuizen had previously been manager at Excelsior in the Netherlands, where his side finished 15th in the Dutch Eredivisie.
Ex-Republic of Ireland midfielder Carsley will be assisted by Paul Williams and will take charge of the Bees for the first time when they host one of his former clubs, Birmingham City, on Tuesday.
"The club believes Lee deserves the opportunity to step up and help shape Brentford FC's future on the pitch," said a statement from Brentford.
Dijkhuizen's departure comes just days after he said he "felt no pressure" about his job despite Brentford's stuttering start to 2015-16.
His final game in charge at Griffin Park was a 2-1 defeat by Sheffield Wednesday, the club's third at home in all competitions this season.
"A chaotic start to English management comes to an abrupt end for Marinus Dijkhuizen.
"During his brief tenure, he has had to deal with matters out of his control, such as problems with the pitch leading to a postponed fixture.
"On the pitch it has been far from a successful spell, with last season's Championship play-off semi-finalists winning just two of their opening eight league games.
"In his defence, Dijkhuizen has been unlucky with injuries and has had to deal with the departure of some key players. His undoing may well be that he was indeed too honest in interviews with the media, something that may well have irked owner Matthew Benham.
"Question marks also hovered over whether he had a strong enough relationship and rapport with players who he didn't sign."
Brentford have sacked head coach Marinus Dijkhuizen after nine matches and placed Lee Carsley in charge until the end of the season.