The Djokovic family did not enjoy any success at their home tournament this year.
With defending champion and top-ranked Novak Djokovic having pulled out of the event, his brother Marko lost in the first round to Filippo Volandri on Monday.
Marko Djokovic, a wild-card entry, was broken four times and never forced a break point of his own before losing 6-3, 6-1 in one hour.
The tournament is organized by the Djokovic family, but Novak pulled out because of the recent death of his grandfather - a decision he called one of the hardest of his career.
In other first-round matches Monday, Dusan Lajovic of Serbia defeated fellow wild-card entry Evgeny Donskoy of Russia 7-5, 6-4, and Ivan Dodig used six breaks of serve to overcome Adrian Ungur of Romania 6-2, 6-7 (4), 6-4.