The 20-year-old centre-half has made 12 senior appearances for the Town after progressing through the youth ranks, with his four starts this term all coming in the Checkatrade Trophy.
Musonda, who captained the Town youth team to a league and cup double success and on a run to the FA Youth Cup quarter-finals in 2015-16, will link up with his team-mate from that side, Craig King, the goalkeeper who left Kenilworth Road last summer and has recently started playing again.
He will also work under former Hatters player and academy coach Joe Deeney, who is assistant-manager at Court Place Farm.
Oxford are currently 17th in the Step 2 division and involved in a fight to avoid relegation, so Frankie – who netted the Hatters' winner in Tuesday night's 1-0 Beds FA Senior Cup semi-final against Bedford Town – will gain more valuable experience following his loan at Braintree Town last season.