Alexander was drafted by the San Francisco 49ers with the eighth pick in the first round of the 1963 NFL Draft. He was also drafted by the Denver Broncos of the American Football League with the fifth overall pick, but chose to sign with San Francisco. Alexander played alongside Pro Football Hall of Fame cornerback Jimmy Johnson. Alexander was selected to play in the Pro Bowl in 1968, after a season in which he had a career-high nine interceptions, including an interception he returned 66 yards for a touchdown.
Alexander played for the 49ers from 1963 to 1969.
In his second year with the Los Angeles Rams in 1971, he returned one of his three interceptions 82 yards for a touchdown. He played one final season with the Philadelphia Eagles in 1973.
Kermit was responsible for injuring Gale Sayers's right knee in a rolling tackle which shortened the career of the Bears star running back, and cost Sayers some of his extraordinary quickness.
In addition to playing defense, Alexander returned punts and kickoffs for all three teams. Both of his career punt returns for touchdowns came with San Francisco.
Alexander was initially planning on adopting one child from Haiti, but after meeting the child's four siblings, he ended up adopting all five. The five were in Haiti at the time of the earthquake in 2010, but survived and now live with Alexander and his wife, Tami.