A statement released by the band on Tuesday states that Johnson, 68, has been "advised by doctors to stop touring immediately or risk total hearing loss."
The band's U.S. shows from March 8 in Atlanta through April 4 in New York City will now be rescheduled for later in the year, "likely with a guest vocalist," according to the release.
"More information regarding these rescheduled shows to come," the band's announcement says. "Current ticket holders can hold on to their tickets for the rescheduled dates or receive a refund at point of purchase."
The Rock or Bust tour began in April 2015, and took the group to countries like Germany, Scotland and Denmark.
Johnson's hearing problem is the latest difficulty to hit the rock band. In September 2014, Malcolm Young, the group's rhythm guitarist and founding member, was forced to retire because of dementia.
How Well Do People Know Their Rock 'n' Roll Icons?
Last July, drummer Phil Rudd was sentenced in New Zealand to eight months of home detention for threatening to kill his former employee.
Rudd, 61, later appeared before a judge in Wellington, New Zealand, to plead not guilty to breaking the rules of his home detention sentence by drinking alcohol.
In February 1980, the band's original frontman Bon Scott died at age 33 from acute alcohol poisoning in London, according to his death certificate.