Those schools with more control over their admissions selected advantaged white, middle-class pupils who were more likely to succeed, he claimed.
The government said schools were required to promote community cohesion.
Mr Johnson said research suggested it was increasing in schools and called for urgent action to reverse the trend.
Steps could include offering cash incentives to encourage schools to take more ethnic minority pupils.
Mr Johnson added: "If a Muslim child is educated in a school where the vast majority of other children are also Muslim, how can we expect him to work, live and interact with people from other cultures when he leaves school?
"This is a ticking time-bomb waiting to explode."
The CRE was particularly concerned about Academy schools and those with Trust status, which had different entry procedures to other state schools.
