After the first attack, the two young men moved to another park where they proceeded to throw two more homemade firebombs at migrants, police said.
The two men were arrested and charged with a number of criminal offenses, including violating laws on weapons and explosives, racism, and causing bodily harm.
On Sunday, a group of nearly 300 refugees, mainly from Afghanistan, Syria and Iraq, staged a protest on Lesbos against the local authorities' failure to process their applications fast enough, so that they could travel onward to mainland Europe.
In recent days, clashes between police and refugees on the island have become a frequent occurrence.
According to preliminary data by the EU border agency Frontex published on Tuesday, over 23,000 migrants arrived in Greece by sea last week, a nearly 50 percent rise on the previous week.
