Wednesday's League Cup defeat at Bradford was Leeds' third in succession, and Hockaday's departure has been announced less than 24 hours later.
Assistant manager Junior Lewis has also left the club, and Neil Redfearn will take charge of the first team until owner Massimo Cellino appoints a permanent successor.
Former Forest Green boss Hockaday was a surprise choice to replace Brian McDermott back in June but won two of his first three games.
Defeats to Brighton and Watford followed, though, and Cellino admitted after the second of those he had considered sacking Hockaday.
The stay of execution proved short, and Cellino said: "The results since the start of the season have meant we needed to act and make this decision.
"After the defeat at Bradford I realised that my decision to keep David at the club following the defeat at Watford was wrong, and I had to change my mind on the coach's position.
"As a club we will now begin our search for a new head coach."
Leeds skipper Jason Pearce took to Twitter to give his reaction to the sacking of Hockaday, posting simply: "Disappointed."
Sky Bet have installed former Catania manager Rolando Maran as the early favourite in their next Leeds manager market. There are also suggestions former West Brom boss Steve Clarke will be considered for the role.
But Leeds great Johnny Giles says Cellino should put himself in charge of the team.
"I don't think anybody would be a good choice," he told Irish radio station News Talk.
"I think this fella is a headbanger, that owner; I think he only employed that coach (Hockaday) so that he could pick the team, bring the players in that he wants.
"No manager worth his salt will touch that job. This fella should make himself manager and pick the team himself. He employed this lad from nowhere, paying him buttons apparently."