Maxwell wrote in a statement for his website: "I know this sucks but after many months of recording I've temporarily damaged my voice. I've had issues before during other tours, but was able to power through. I've been strongly advised to rest and undergo treatment.
"I look forward to hopefully seeing you next on our full fledged tour, when the sequel to the BLACKsummers'night trilogy is released. My deepest apologies to those who made the effort to try and see the show."
Refunds will be available for all six dates in Los Angeles, Atlanta and Newark.
Maxwell's last studio album BLACKsummers'night was released in 2009.
Watch Maxwell's 'This Woman's Work' music video below: