The 31-year-old was allowed to leave on Sunday after passing a concussion test, a spokesman for Bochum said.
The keeper, who was unable to keep on playing, has suffered from nausea, headaches and discomfort since the incident on Saturday, with the lighter being thrown from the Union fans' end.
Drewes sat out training on Sunday and Bochum have Monday off. His progress will be monitored, the spokesman added.
The alleged perpetrator is being held on suspicion of grievous bodily harm, Berlin police said.
The 27-year-old was located by security after the incident at the An der Alten Forsterei stadium and handed over to police. The man was arrested and has also given a blood test.
German Football Federation (DFB) referee instructor Lutz Wagner has praised the behaviour of match official Martin Petersen during the controversial Bundesliga game.
The match was interrupted late on because of the lighter incident. The referee took the players off and they returned after 25 minutes to play out a 1-1 draw.
Bochum, bottom with no wins this term, have since said they will challenge the result at the DFB and believe the referee should have called off the game. Wagner thinks otherwise.
"The referee behaved correctly because he sent the teams to the dressing room to give the stewards the opportunity to control the situation," former referee Wagner told Sportschau.
Bochum managing director Ilja Kaenzig criticised accusations that Drewes was pretending he was hurt after being hit by the lighter.
"The atmosphere was heated. There were ugly comments, not only in the stands, but also in the tunnel, where accusations of acting were made," he told Bild TV.
Kaenzig didn't say who exactly made these accusations, only speaking of "those present in this area."
"It's unacceptable for one of our players to be hit and then have to justify why he wasn't more seriously injured," the managing director said.
It was a bad day for German football with the late Bundesliga game between St Pauli and Werder Bremen suspended for almost 10 minutes in the second half due to pyrotechnics.
Both sets of fans camps set off huge amounts of banned pyrotechnics in the Northern derby and both clubs are likely to face fines following Bremen's 2-0 win.