Sri Lanka have lost four ODIs on the trot against South Africa.
Karunaratne was hit on the neck by a bouncer from pacer Pat Cummins.
Sri Lanka once again made a losing start to a tour having lost the opening Test in Australia at the Gabba by an innings and 40 runs.
Rixon is expected to join the team in New Zealand on the 24th of December.
"This breakdown of communication needs to be sorted quickly."
Sri Lanka have won the Asia Cup as many as five times.
The 34-year-old last donned the national colours last year in a T20I against India.
ICC will now have to appoint the judicial commissioner to hear the case.
Sri Lanka is set to tour West Indies in the last week of May for three-match Test series.
The new coach is expected to take over the duties before the Nidahas Trophy.