The visit comes as Moscow's offensive crosses the four-and-a-half-year mark and as the war between the neighbours intensifies this summer, with US-brokered peace talks frozen.
In a video released by the ministry, Gerasimov said Russian forces were advancing on the east Ukrainian town of Sloviansk and praised their "successes".
"The offensive is proceeding at an unabated pace on all fronts," he said. "There are four kilometres left to the eastern suburbs of Sloviansk." AFP could not independently verify the claim.
Russia has not eased its maximalist demand that Ukraine cede the rest of the east, with the Kremlin tasking troops with taking control of the whole of the Donetsk region.
Sloviansk and nearby Kramatorsk are the last major hubs under Ukrainian control in the Donetsk region, part of the so-called fortress belt -- a chain of heavily fortified defence lines built by Kyiv since 2014.
Sloviansk has been a symbol of Ukrainian resistance since 2014, when it was held for around three months by pro-Russian separatist forces before Kyiv retook it.
On Wednesday, Ukrainian President Volodymyr Zelensky appointed Andriy Biletskyi and Denys Prokopenko -- widely seen as among the country's best commanders -- to lead the region's defence.
