Harris was arrested in 2017 for marijuana possession and served two days in jail this March after reaching a plea deal.
He was originally charged with Class A possession of marijuana and a Class D misdemeanor of drug paraphernalia in Bates County, Missouri before the plea. He was also given two years of probation, 80 hours of community service and a $500 fine as part of the deal.
The former undrafted free agent has been a valuable part of the Chiefs offense over the past four years, appearing in all 16 games over the last three seasons.
Harris finished last year with 18 catches for 224 yards, both of which were career highs.
While Travis Kelce remains the top option at tight end for the Chiefs, his suspension could open the door for more playing time for Tim Wright or Jace Amaro.
The Chiefs are set to face the Los Angeles Chargers on the road in Week 1 on September 9.