A hiker who was walking on one of the mountain's many trails was killed, and two other people were reported injured, according to Italy's Civil Protection Agency.
Frightened tourists threw themselves into the surrounding waters to escape the flying debris, the Italian news agency, ANSA, reported. The national fire department was dispatched to help bring stranded hikers down.
Two lava flows were also created on the side of the volcano, but there was no reported threat to any structures.
The hot lava pebbles flung from the crater set off fires on the slopes of the volcano. The Civil Protection Agency and Fire Department were hampered by the thick smoke while trying to fight the fire.
Marco Giorgianni, the mayor of the island's principle town, Lipari, said there was little damage to the residential areas of the island and no need for evacuation, but offered assistance to anyone wishing to leave, according to Italian paper La Repubblica. The island is only accessible by ferry.
Planes were flown from the mainland to try and extinguish the fires that were burning dry brush on the slopes of the volcano.
Stromboli is an active volcano, and the last time was erupted was in the summer of 2014, according to Volcano Discovery. Other lava flow eruptions took place in 2007 and 2002 into 2003.
Stromboli, which is north of Sicily and west of the mainland region of Calabria, is a popular summer destination as part of the Aeolian Islands and is full of tourists at this time of year. Last week, the island hosted its annual candlelight theater festival.