Google users whose searches were disclosed to others didn’t suffer enough of an injury to sue the internet company, the government will tell the U.S. Supreme Court Oct. 31.

The court Oct. 1 granted Solicitor General Noel J. Francisco’s motion to participate in the oral argument.

The government’s position could derail the argument of frequent class objector Ted Frank of the Competitive Enterprise Institute in Washington. Frank wants the court to consider whether an $8.5 million settlement in the case was fair, given that none of the funds go to class members, and most goes to charity.

The $5.3 million...