The fashion brand has been a sponsor of McLaren for more than 30 years before it switched to Mercedes in 2015, but chief executive Mark Langer says they will now switch to sponsoring Formula E in the future, though didn't confirm with which team.
"Of course Formula 1 is the premier class of motor racing, but Formula E is more innovative and sustainable," Langer told German magazine Focus.
"The engines, the races in big cities, that appeals to a younger audience and opens up new possibilities.
"But after many years in Formula 1, actually since Jochen Mass in the seventies, we've been wondering what's the next thing? What's next [for Hugo Boss]."
It comes as Mercedes along with other leading manufacturers such as Porsche, have confirmed their involvement in the all-electric racing series.