The prime minister told the Swedish Parliament's Committee on European Union Affairs that if the 28-member bloc isn't able to get a hold on the situation it could very well jeopardized the entire union.
"We are facing a humanitarian disaster," he said. "The EU must be able to help Greece manage this enormous stress facing the country."
Greece has taken in about 120,000 refugees during the first two months of the year and, with neighboring Macedonia closing its borders, many of them have begun piling up inside the country.
Löfven pledged, among other things, prefabricated homes and tents to Greece to house migrants. It is unclear how many houses and tents will be sent and when they would arrive.
Sweden's prime minister will head to Brussels on Monday for an EU summit that is hoping to find a joint European solution to the ongoing refugee problem.