The results announced Thursday showed 87% of workers voted in favor of the strike authorization.
This does not mean workers are hitting the picket line, however.
DC 33 says the vote simply gives union leaders the authority to call a strike at any time.
District 33 has vowed to give a 10-day warning about any strike.
The union represents at least 9,000 mostly blue-collar employees, including sanitation workers.
They have been working without a contract since July.