With interim first-team manager Michael Appleton watching on, Muskwe grabbed a 13th-minute opener when his header slipped through the hands of Swansea goalkeeper Gregor Zabret.
Swans centre-back Jack Bainbridge was dismissed for a high challenge just before half-time, and Muskwe doubled the lead in the 59th minute from substitute Liandro Martis's cross.
Leicester, who are now unbeaten in six matches across all competitions, visit Division 1 leaders Liverpool next on Sunday 29 October. Swansea host Everton at their training ground on Friday 27 October.
(Photo courtesy of Plumb Images/LCFC)