The move came hours after the government of Prime Minister Viktor Orban said it would end a poster campaign attacking Soros that has been accused of anti-Semitism.
Brussels also announced that it is advancing a separate case over an education law that could shut a Soros-backed university, risking a fresh confrontation with Orban.
"We have studied the new law on NGOs carefully and have come to the conclusion that it does not comply with EU law," European Commission Vice President Frans Timmermans said.
"We await a reaction from the Hungarian authorities within a month."
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Hungary's parliament approved the law last month which will force groups receiving more than 24,000 euros (USD 26,000) annually in overseas funding to register as a "foreign-supported organisation", or risk closure for non- compliance.
They will also have to use the label "foreign-supported organisation" on their websites, press releases and other publications.
Orban's government says the measures are aimed at improving transparency as well as fighting money laundering and terrorism funding.
"We expect a reaction from the Hungarian authorities within a month. If the response is not satisfactory, the commission can decide to go to the court," Timmermans said, referring to the European Court of Justice, the EU's top judiciary body.
Budapest has been outspoken in its opposition to Soros, claiming that his donations of billions of euros (dollars) to rights groups in the region are a bid to force Hungary to take in migrants.