Sneed sustained the injury during Monday night's game against the Baltimore Ravens.
Asked for a timeline on Sneed's recovery, coach Andy Reid said Wednesday, "We'll see how that works, as far as time away.''
Putting Sneed on injured reserve will sideline him for at least three weeks.
Sneed, a fourth-round draft pick from Louisiana Tech, has been a pleasant surprise for the Chiefs. He started the first three games and is tied for the NFL lead in interceptions with two.
His rapid development has been an important factor in the Chiefs' 3-0 start.
Ward replaced Sneed after the injury against the Ravens and played with his hand heavily wrapped.
The nature of Sneed's injury was first reported by the Kansas City Star.