Djukic, 47, has finally paid the price for overseeing a disappointing start to the season that has delivered only 20 points from 16 league games, culminating in Sunday's 3-0 defeat to Atletico Madrid.
In a press conference televised on the club's official website, Djukic said he was the only one to blame for the decision.
"I have not managed to put Valencia where I said when I arrived, so I'm the one to blame," he said.
Club president Amadeo Salvo confirmed 33-year-old Estevez had assumed Djukic's responsibilities while a permanent successor is sought.
Los Che were Spanish champions as recently as 2004 but have lost five of their last nine league games and sit ninth in the La Liga table ahead of Saturday's home meeting with Real Madrid.
Serbian Djukic won promotion with Real Valladolid in 2011 and replaced Ernesto Valverde at Mestalla in June, but came under pressure during the early days of his reign.
Three straight wins in September appeared to stabilise his position, yet Valencia would not win in October and picked up only four points the following month before a 3-0 win over Osasuna briefly glossed over the poor run.
Sunday's defeat at Atletico meant Djukic's card was marked.
Their domestic struggles have, however, contrasted sharply with an impressive Europa League campaign, in which Djukic's men shrugged off an early loss to Swansea to win their group at a canter.
Estevez, or a permanent successor, will tackle Ukrainian giants Dynamo Kiev over two last-32 legs in February.