World number one Djokovic received a standing ovation from the home crowd by the Danube river in the Serbian capital after an erratic display against world number 255 Molcan, who battled through from the qualifying rounds.
Djokovic also lost to Russian Aslan Karatsev in the Serbia Open semi-finals before being defeated by Rafael Nadal in the Rome Masters final and his display against Molcan was at times unconvincing.
"Unfortunately, there will be no fans this year as we're in a difficult situation with a lot of people contracting the virus on a daily basis," the ATP 250 event's organiser Djordje Djokovic told Serbia's Nova S television.
"It's a very difficult year for everyone and the restrictions have resulted in a lot injuries. Regrettably, Borna Coric and Stan Wawrinka have had to pull out but it's still going to be a very strong field.