The actress met Tribes guitarist Dan 'Skywizard' White while filming in London and has been seeing him for the past few weeks.
"They met in London recently. Scarlett was shooting the film Under The Skin in the UK and they were introduced at a club night in town," a source told the Sunday Mirror.
"They got on like a house on fire and Scarlett was into his band's music. There was an instant connection. They've been seeing each other for a good few weeks. Dan's proper happy about it - and what guy wouldn't be? He already thinks the world of Scarlett.
"Dan thinks she's an amazing girl. They both have incredibly busy lives but are going to see where things go. Dan's band Tribes is only just taking off and Scarlett has a lot of work on. So who knows?"
Johansson split from husband Ryan Reynolds in July and has since been romantically linked to Sean Penn, Bradley Cooper and Justin Timberlake.