The baby boy was taken to hospital on the nearby island of Samos, where he was pronounced dead.
Greece is struggling to cope with the hundreds of migrants and refugees from the war in Syria making the short crossing every day from Turkey to Greece's eastern islands, including Kos, Lesbos, Samos and Agathonisi. Thousands are waiting to be identified and ferried to Athens to continue their trip to other European countries.
Read: Migrant child's body on beach shocks Europe
European Commission First Vice President Frans Timmermans and Migration Commissioner Dimitris Avramopoulos have promised Athens 33 million euros to help it tackle the migration crisis.
Former Greek premier Alexis Tsipras, who resigned last month to prepare for a snap election on Sept. 20, and his main conservative rival Evangelos Meimarakis are fighting an unexpectedly tight election campaign and traded barbs on Friday over the issue.
Read: Turkey arrests 'four traffickers' over migrant toddler's death
Avramopoulos, in Athens, urged the parties on Saturday to avoid politicising the issue.
"With all my heart, I hope that the government that will take over after the elections will tackle the major economic issues along with the migration and refugee issues prudently and with responsibility," he said after meetings with Greek President Prokopis Pavlopoulos and Interim Prime Minister Vassiliki Thanou.
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