Werder were beaten 4-1 by Borussia Moenchengladbach and have yet to earn a point this season, with the 46-year-old Ukrainian leaving after almost two years in charge.
Werder had also been eliminated from the German Cup in the first round by third tier club Sportfreunde Lotte.
"The preparation for the two home games against Mainz 05 and VfL Wolfsburg is taken over on Monday by Under-23 coach Alexander Nouri," Werder said in a statement.
Skripnik's assistant coaches Torsten Frings and Florian Kohfeldt were also let go.
"We decided to take this step because we were not convinced after the Gladbach game that the current setup was capable of turning things around in the short term," said Werder sports director Frank Baumann.
(Reporting by Karolos Grohmann; editing by Sudipto Ganguly)
