Born in Fort Erie, Ontario, Brenneman played OHA junior hockey in the Chicago Black Hawks organization, playing for the St. Catharines TeePees from 1959 through 1962 and the St. Catharines Black Hawks in 1962–3. While still in his final year of junior he played 4 games for the AHL's Buffalo Bisons, scoring a goal.
The next season saw Brenneman post impressive offensive totals with the St. Louis Braves of the CPHL. In 1964–65 he split the season amongst the Braves and two NHL teams, the Chicago Black Hawks, for whom he appeared in 17 games and scored a goal, and the New York Rangers, collecting 3 goals and 3 assists in 22 contests.
Brenneman remained in the Rangers organization for the following season, going scoreless in 11 games with the parent club while playing again in the CPHL for the Minnesota Rangers and the AHL with the Baltimore Clippers. For 1966–67, Brenneman played split time between the AHL's Rochester Americans and NHL's Toronto Maple Leafs. He played 43 regular season games for Toronto, qualifing to be on the cup. However, John's Brenneman name was left off the cup, because he was sent to the minors before the playoffs.
Brenneman spend the following seasons split between the Detroit Red Wings origanization, where he played 9 games and scored 2 assists for the parent club, and the Oakland Seals, for whom he appeared in 31 games and scored 10 goals and 8 assists in 31 games. He remained with Oakland for the following season, scoring a goal and collecting 2 assists in 21 games. Following a season when did not play pro hockey, Brenneman played 1970–71 in the IHL with the Dayton Gems, scoring 41 points in 50 games.