Some 51 Russian tourists were on the bus, ekathimerini reported.
The accident occurred about 4:30 a.m. local time in the town of Nea Moudania as the bus travelled to Makedonia Airport in Thessaloniki.
Rain had earlier fallen in the area.
Some 33 adults and four children were taken to an area hospital for treatment, ITAR-Tass reported.
Twenty passengers were treated and released, the hospital director said. Two adults and a child underwent surgery.