The warrant concerns his alleged role in a coup attempt in Burkina Faso in September, which sparked deadly street protests.
Authorities listened to phone recordings linking Mr Soro to the coup, Reuters news agency says.
Mr Soro has always denied that his was the voice on the tape.
The speaker is an ally of Ivory Coast President Alassane Ouattara.
Mr Soro and the armed rebel group he led - the New Forces - played a key role in Ivory Coast's 2011 civil war.
"I confirm that the warrant was issued at the beginning of the week," a military source told Reuters.
Former Burkina Faso Prime Minister Isaac Zida previously confirmed that Mr Soro's voice was heard in a recording advising former Burkinabe foreign affairs minister Djibril Bassole on how to be successful in a coup.
In September, presidential guard officers seized power in a coup, overthrowing Burkina Faso's interim government.
Members of the presidential guard - set up by ex-President Blaise Compaore - said they were unhappy with the new electoral law banning candidates linked to a bid to extend the president's time in office. The attempt triggered his overthrow in October 2014.
But the coup ended just over a week later, and the reinstated interim government disbanded the presidential guard.
Burkina Faso has issued an international arrest warrant for Guillaume Soro, Ivory Coast's speaker of parliament.