Lee lost the election by 114 votes out of about 25,000 cast, according to an official at the Orange County Board of Elections.
The recount will begin Monday morning at 9 a.m. and continue until all votes are counted. North Carolina election law does not provide for automatic recounts, but one is presumed in tight races.
"Out of respect for people who supported me, I need to show that I made every effort," Lee said Wednesday of the possibility of a recount.
Kinnaird and Lee were pitted against each other in the Democratic primary after a judge ruled that the N.C. General Assembly's original redistricting plan violated the state constitution.
Both Kinnaird and Lee serve on the Senate Appropriations Committee, which is responsible for drafting a version of the budget to be considered by the full chamber. Lee serves as Appropriations Committee chairman.
Kinnaird, a former Carrboro mayor, is serving her third term in the Senate.
Lee, a six-term senator, was mayor of Chapel Hill from 1969-75. He was the first black mayor in North Carolina.
