Associate head coach Stephen Silas, as he did during Monday's win over Orlando, will take over as head coach during Clifford's absence.
The team says there is no timetable for Clifford's return and would have no further comment.
Saudi-led coalition intensifies Yemen air strikes after Saleh's death
Speaking before a gathering of supporters, al-Houthi says: "We knew that they were deceived. we hadn't hoped for what happened". He was killed by the rebels on Monday, leaving his followers in disarray.
The Hornets are now 9-13 this season and are in 11th place in the Eastern Conference.
Silas will continue to coach the team with Clifford out.
Silas received a text message at about 2 p.m. Monday saying Clifford was too sick to coach the team that evening, the Charlotte Observer reports. Charlotte's next game is against the Golden State Warriors, and a road trip featuring the Oklahoma City Thunder and Houston Rockets follows two other home games. But the Hornets can't be blamed for not offering specific details at this point.