Tunisia international Mejbri was referred to an independent regulatory commission after spitting in the direction of visiting Leeds fans around the 67th minute as Burnley won 2-0, the Football Association said in a statement.
"Hannibal Mejbri subsequently admitted the charge, and the regulatory commission imposed a four-match suspension," it added.
Mejbri was also fined £15,000.
Burnley, 19th in the table, have lost five matches in a row and visit 12th-placed Newcastle United on Saturday.