It passed by 77 votes in last month's election, with 6,003 votes counted.
The recount was requested by Common Sense SeaTac, a business group that opposed the proposition. It also faces a court challenge, led by Alaska Air Group. It questions whether it has authority at the airport, which is operated by the Port of Seattle.
The SeaTac minimum wage campaign drew $1.8 million in spending in the small city, with national labor groups supporting higher pay and national business groups opposing.