A 25-year-old man, with his political asylum documents still on him, was found hanged near a port in Athens.
Greek media described as a Syrian refugee, according to Telesurtv.net.
More than 60,000 refugees and migrants have gone to Greece, and ended up stranded in camps, or living in abandoned warehouses and tents, among other places that international human rights groups have denounced as having substandard conditions.
They have been stranded since most European countries closed their borders to the migrants. The conditions on the camps are so poor, say human rights groups, that many migrants have attempted suicide.
"Under these conditions, tense situations could lead to such unfortunate incidents," Kyriakos Katsadoros, the scientific director of Klimaka's Greek Suicide Prevention Centre, told Al Jazeera.
"And amid such large numbers, there are people who are vulnerable and in need of help — which they often can't find, unfortunately, in Greece.”
Greek officials complained in recent days that they cannot take one more migrant, and that their capacity to hold them has reached its limit.
Greece has received more than a million migrants since 2014.
Most of the migrants come from North Africa and the Middle East.
The United Nation’s International Organization for Migration reports that 20,484 migrants and refugees entered Europe by sea this year through mid-March. More than 80 percent – 16,248 -- of that staggering number arrived in Italy, the second largest-number went to Greece and the third-largest to Spain.