Oltra and assistant Chema Sanz leave a club at the foot of La Liga with just two wins from 17 matches this season.
Club president Augusto Cesar Lendoiro announced the news at a press conference held at the club's stadium.
According to Deportivo's official website, Lendoiro said: "We felt that now was the right time for a change.
"In the next few hours, or even tomorrow [Monday], we hope to introduce the new coach."
Oltra led Deportivo to promotion from the Segunda Division last season, with the team promoted as impressive champions, and they began this season promisingly with an opening win followed by three draws.
However a severe decline in their fortunes followed, and Deportivo went to the winter break on the back of a 2-0 defeat against fellow strugglers Espanyol, leaving them fighting for their lives in the top flight.
They have mustered 12 points so far, leaving them bottom but only three points adrift of the last team in a safe position, 17th-placed Celta Vigo.
Former Braga and Sporting Lisbon coach Domingos was named in Spanish media reports tonight as a possible contender to step in as the new Deportivo boss.