"This was not an easy decision for the board," Wolfsburg's board chairman Francisco Javier Garcia Sanz said in a statement.
"But it was clear that after the negative results of the past weeks we had to act."
German media reported that former Real Madrid coach Bernd Schuster was one of the possible successors. A club spokeswoman would not comment on the likely replacements.
Lorenz-Guenther Koestner, who coaches the Wolfsburg reserves will take over for now, the club said.
Veh, who steered VfB Stuttgart to the title in 2007, replaced Felix Magath at Wolfsburg at the start of the season.
However Wolfsburg are a shadow of the team who romped to their maiden title last year, losing their last three league matches and failing to win since early November.
They dropped to 10th place in the Bundesliga, 17 off the top after 19 games, following their 3-2 defeat against visitors Cologne.
"The cooperation with Armin Veh was good and his ties to the team were good," sporting director Dieter Hoeness said.
"Unfortunately the results did not come. This was a source for much insecurity within the team. We were not convinced any more that the situation could change in the near future with Veh."
Wolfsburg's once rock-solid defence is now the second worse in the league, slightly better than bottom-placed Hertha Berlin, while last season's top striker Grafite has netted only five goals.
"The last nine matches without a win and the high number of goals, with 38 goals against us, are clear signs," said Hoeness.
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
‘England have the players to win the World Cup – it’ll be tough for Thomas Tuchel to do a bad job, with the squad he has at his disposal’ Former Three Lions winger backs new boss after gentle qualifying draw
