"It is completely unacceptable that England players were racially abused in Hungary last night," he wrote on Twitter.
Johnson urged FIFA to take "strong action against those responsible to ensure that this kind of disgraceful behaviour is eradicated from the game for good."
FIFA said it had opened disciplinary proceedings into the incidents at the match and reiterated an earlier statement reaffirming its zero tolerance stance against racism.
British broadcasters reported that Black England players were targeted with racial abuse by some Hungary supporters during Friday's (NZ time) World Cup qualifier in Budapest that England won 4-0.
ITV and Sky Sports said their reporters heard monkey chants being aimed at England forward Raheem Sterling and substitute Jude Bellingham.
Photo file Eurosports Caption: FIFA office