In the fall of 1952, a point shaving scandal involving four Kentucky players (one of whom was a teammate of Ramsey on Kentucky’s 1951 NCAA champions) over a four-year period forced Kentucky to forfeit its upcoming season, Ramsey’s senior year, as well as that of Cliff Hagan and Lou Tsioropoulos. The suspension of the season made Kentucky's basketball team, in effect, the first college sports team to get the "death penalty.", although it was nothing more than the NCAA asking members schools not to schedule Kentucky, and not mandating it.
Ramsey, Hagan and Tsioropoulos all graduated from Kentucky in 1953 and, as a result, became eligible for the NBA Draft. All three players were selected by the Boston Celtics—Ramsey in the first round, Hagan in the third, and Tsioropoulos in the seventh. All three also returned to Kentucky for one more season despite graduating. After finishing the regular season (one in which Ramsey averaged 19.6 points per game) with a perfect 25-0 record and a #1 ranking in the Associated Press, Kentucky had been offered a bid into the NCAA Tournament. However, then-existing NCAA rules prohibited graduate students from participating in post-season play; the Wildcats declined the bid because their participation would have forced them to play without Ramsey, Hagan and Tsioropoulos, thus jeopardizing their perfect season.
Upon completion of his college career, Ramsey scored 1344 points, which at the time ranked him fourth in the school's history, and grabbed 1038 rebounds, a school record later surpassed by one of his future Kentucky Colonel players, Dan Issel.
Ramsey's best statistical season was 1957-1958; he averaged 16.5 points and 7.3 rebounds per game. It was also his only post-military season in which the Celtics did not win the NBA championship; the Bob Pettit-led St. Louis Hawks (who also featured Cliff Hagan, Ramsey's ex-college teammate) defeated them in the NBA Finals.
Ramsey was also a head coach for one season (1970–71) in the ABA with the Kentucky Colonels, who were led by two former Kentucky Wildcats - Issel, a rookie, and Louie Dampier. Ramsey was named coach 17 games into an 84-game season (which began with Gene Rhodes coaching the first 15 games and fellow Kentucky alum Alex Groza coaching the next two) and, though he had a 32-35 record, coached the Colonels into the playoffs. The Colonels lost to the Utah Stars (who were coached by Sharman, Ramsey's ex-Celtic teammate) in the 1971 ABA Finals, 4 games to 3. Joe Mullaney replaced Ramsey as coach the following season.
Prior to coaching in the ABA, Ramsey had been Red Auerbach's first choice to replace his mentor as Celtics coach after Auerbach retired at the end of the 1965-66 season. However, Ramsey decided to move back to Madisonville; his father, Frank Sr., wasn't in good health and Frank Jr. had three children to raise. 
Auerbach is often credited throughout basketball with creating the sixth man. Though Ramsey was one of the Celtics' best players, he felt more comfortable coming off the bench and Auerbach wanted him fresh and in the lineup at the end of close games. Ramsey was the first in a series of sixth men who won championship rings with the Celtics. In the championships the Celtics won after Ramsey's retirement, they have had successful sixth men such as Havlicek, Paul Silas, Kevin McHale, Bill Walton and James Posey.
Ramsey was mentioned in an episode of Married... with Children. Bud asked Al the trivia question, "Who was known as the best sixth man in basketball? He played for the Celtics," to which Al nonchalantly replied, "Frank Ramsey". However, little did Al know that Bud was answering a $100 trivia question from the television.