Plume of smoke has risen 20km (12 miles) into the sky from the volcano.
But Iceland's Meteorological Office says the eruption should not cause widespread disruption to air traffic.
Last year, ash clouds from another Icelandic volcano, Eyjafjallajokul, led to the closure of a large section of European airspace.
Governments feared that ash particles could cause aircraft engines to fail, and the closure caused chaos to air travellers.
Different ash
Hjordis Gudmundsdottir, a spokeswoman for the Isavia civil aviation authority - which has imposed a flight ban of 120 nautical miles (222 km) around Grimsvotn - said: "We have closed the area until we know better what effect the ash will have."
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Glaciologist Matthew Roberts: the eruption "shouldn't have any far-reaching effects"
But officials say it is unlikey to have the same impact as last year.
Pall Einarsson, a geophysicist at the University of Iceland, said the 2010 eruption was a rare event.
Icelandic Met Office website reported that ash is falling in the vicinity of the Vatnajokull glacier. This also includes towns of Hofn i Hornafirdi and Kirkjubaerklaustur as well as farmland nearby. The plume is up to 12 miles (20km) high, but the basalt eruption is meant to give the ash a density that will prevent a Eyjafjallajokull-style spreading.
Other effects associated with Grímsvötn is glacial flooding. As lava protrudes the Vatnajokull glacier and the ice is melted, water is produced.
There has been some confusion about this eruption. Icelandic authorities have found themselves disambiguating to the global media that Grímsvötn is not the more powerful Eyjafjallajokull, which disrupted air traffic last year. Although Grímsvötn Volcano has interrupted air traffic in the past, it has never downed international flights. This particular eruption is not expected to interrupt European air traffic in the next 24 hours.
Authorities were reportedly reassuring the nearby locals that there is no need for evacuations.
According to the Smithsonian National Museum of Natural History, in 1783 this very volcano's 16.7 mile long fissure system (known as 'Skaftar') "produced the world's largest known historical lava flow during an eruption". It lasted for seven months and damaged crops and livestock. This in turn also caused a famine resulting in the death of one fifth of Iceland's population.