The band's official website announced that Greenfield died on Sunday after contracting the virus following a stay in a hospital for heart problems.
Bass player Jean-Jacques “JJ” Burnel paid tribute to Greenfield as a “musical genius," who had “passed away as one of the victims of the Great Pandemic of 2020.”
Greenfield was known for his distinctive sound and playing style, using instruments such as the harpsichord and Hammond electric organ.
He joined the band in 1975, which subsequently became one of the most innovative during Britain's punk explosion in the late 1970s. It had recently postponed a farewell tour from this summer because of the pandemic.
Greenfield is survived by his wife Pam.