The complaint signed by five lawmakers from the Left and Green parties is the first of its kind in Sweden against a head of state, writes AFP.
The suit relates to the conflict in Turkey's Kurdish majority south-east, which has been battered by renewed fighting between Kurdish rebels and Turkish security forces since a fragile truce collapsed in 2015.
“We are five lawmakers handing in a complaint… (requesting) punishment for genocide, crimes against humanity and war crimes,” Annika Lillemets, an MP for the Green party, told a news conference in Stockholm.
The complaint, filed to the Swedish International Public Prosecution Offices, names Erdogan and several ministers including Prime Minister Binali Yildirim.
A Swedish law adopted in 2014 allows the country's courts to judge cases of alleged crimes against humanity regardless of where they have been committed or by whom.
The law stipulates that “anyone, who in order to completely or patially destroy a national or ethnic group of people” kills, causes serious pain or injury is “guilty of genocide”.
The Public Prosecution Offices said it would now decide whether to initiate a preliminary investigation, adding that “it may take a while”.
If prosecutors decide to launch an investigation, Erdogan could risk an arrest warrant in Sweden, the lawmakers said.
Carl Schlyter, an MP for the Greens, said he hoped other lawmakers in European countries would follow their move.
“If (Erdogan) is hindered from roaming around in Europe and influencing European countries the way he wants, then I hope that this will affect his politics,” he said.
The UN Human Rights Office in March released a report on allegations of “massive destruction, killings and numerous other serious human rights violations committed” between July 2015 and December 2016 in Turkey's south-east.
Hundreds of members of the Turkish security forces have been killed since the collapse of the ceasefire, and the army has claimed killing thousands of militants.
The Kurdistan Workers' Party (PKK), classified as a terror group by Turkey, the EU and the US, has waged an insurgency in the country since 1984 – initially focusing on independence demands then greater rights – that has left at least 40,000 people dead.