He passed away during treatment at the capital's United Hospital on early Wednesday.
Zafar had been battling several health issues, including a kidney ailment, for a long time. He was admitted to the Bangabandhu Sheikh Mujib Medical University a few days ago.
CPB President Mujahidul Islam Selim, General Secretary M Shah Alam and fellow political leaders rushed to the hospital after hearing of Zafar's demise.
He will be buried at his birthplace in Moulvibazar, the party members said.
Syed Abu Zafar Ahmed was re-elected general secretary in the party's congress in 2016 before quitting his position the next year due to illness. He was later inducted into the party's presidium.
Born in Moulvibazar on 11 Jul, 1958, Zafar had been a prominent political activist from his student days. He gained admission to the Dhaka City Law College after his graduation from Moulvibazar Govt College before pursuing his higher education in Germany.
Zafar spent a year in prison following his protests against the murder of Bangabandhu Sheikh Mujibur Rahman in 1975. He was also jailed for his part in the movement to remove the military rule of Ershad.