"We are aware of the incident, will gather more information and handle this matter appropriately," a team spokesman said.
The citation occurred in Westlake, Ohio, about 10 miles from the Browns' practice facility.
According to the service report released by Westlake police, the two were pulled over just before 9:30 a.m. ET and were each written $124 tickets. Police also conducted a probable cause search in one of the vehicles for a suspected marijuana joint, according to the report. Police didn't specify which vehicle had the suspected joint, and neither Higgins nor Willis was cited for it.
Police did not specify how fast either was driving.
Cleveland's players were off Tuesday.
Wills, the No. 10 overall pick in the 2020 NFL draft, has started all but one game at left tackle for the Browns this season.
Higgins has emerged as a key target for quarterback Baker Mayfield late in the season.
On Tuesday evening, Higgins posted on Twitter that his "foot slipped," in regard to the drag racing citation, before deleting the tweet. He also posted he "was tryna get away from Covid," before deleting that tweet, as well.
Wills wrote on Twitter that people were "Blowing it way out of proportion."
The Browns were slammed with more COVID-19 trouble on Tuesday, as coach Kevin Stefanski, wide receiver KhaDarel Hodge and Pro Bowl guard Joel Bitonio all tested positive for the virus, knocking them out of Sunday's playoff game at the Pittsburgh Steelers.