The Raggae Boyz face El Salvador on Sunday and Guatemala three days later although JJ will only take part in the first game, both of which are to be played in Kingston.
Wednesday face Queens Park Rangers next Saturday and Owls boss Brian Laws is worried that the ten-hour flight and the subsequent jet-lag would not be ideal preparation for the former Bradford man for the Loftus Road clash.
Johnson has blown hot and cold this season although he seems to be on form at the moment and The Owls' boss is not wanting to risk him in a friendly game for his country when he is needed fresh for Wednesday's resurgent climb up the table.
Deon Burton will have no such restrictions about being picked in the games after he missed out on being named in the squad.
Meanwhile, a strong Owls reserve side including Kenny Lunt, Yoann Folly, Mark Beevers and Wade Small were beaten by Barnsley's second string 1-0 yesterday.