The Swiss club said in a statement that the German had been replaced by Murat Yakin, who led Lucerne to second place behind Basel in both the league and cup last season and was dismissed in August after a poor start to the current campaign.
Basel have struggled this season after a flurry of departures.
Winger Xherdan Shaqiri joined Bayern Munich and Granit Xhaka, like Shaqiri a Swiss international, moved to Borussia Moenchengladbach. Former captain Benjamin Huggel retired.
Basel also sold Argentine central defender David Abraham to Spanish side Getafe.
The Swiss club brought on board Egyptian rising star Mohamed Salah who made an immediat impact but couldn't lift the champions past their struggle.
Basel, who beat Manchester United last year to reach the Champions League knockout stages, missed out on this year's competition after losing to Romanian side FC Cluj in the playoff round.
They lie fourth in the Swiss Super League, eight points behind leaders Grasshoppers after 12 matches of the 36-game campaign.
The 36-year-old Vogel, a former minor league player, was previously assistant to Thorsten Fink and was promoted one year ago after his fellow German left to coach Hamburg SV.
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