Volcanologist Magnus Tumi Gudmundsson told The Associated Press that the eruption appeared to be small.
"But we don't know where in the process things are at," he said as he boarded a helicopter for a first look.
The 2021 eruption in the same area produced spectacular lava flows for several months. Hundreds of thousands of people flocked to see the spectacular sight.
Iceland, located above a volcanic hotspot in the North Atlantic, averages an eruption every four to five years.
The most disruptive in recent times was the 2010 eruption of the Eyjafjallajokull volcano, which sent clouds of ash and dust into the atmosphere, interrupting air travel for days between Europe and North America because of concerns the ash could damage jet engines. More than 100,000 flights were grounded, stranding millions of passengers.
Shares in Iceland's flagship airline, Icelandair, rose 6 per cent when news of the eruption broke Wednesday. Investors and residents alike had been spooked by the possibility of a much more disruptive eruption in a populated area of the peninsula.