With more than 90 percent of the votes in, Wicker led by almost 120,000 votes, the Biloxi Sun Herald reported. He had 56 percent of the vote to 44 percent for Musgrove.
Wicker claimed victory late Tuesday, but Musgrove did not concede, saying that not all the votes were counted.
Because of the special election, Mississippi had two Senate races this year. Thad Cochran won a fifth term easily.
The Wicker-Musgrove race was an expensive one on both sides. Between contributions from national party committees and spending by the two campaigns, the two sides spent well over $10 million.