Uche, 26, has two sacks in six games this season and 20.5 sacks in his career.
Uche re-signed with the Patriots as a free agent before the season on a one-year, $3 million contract. He will be an unrestricted free agent after this season.
It's the second impact trade made by the Chiefs (7-0), who acquired wide receiver DeAndre Hopkins in a deal with the Tennessee Titans last week.