Draper, a trade union leader and strong supporter of Labour Party leader Jeremy Corbyn, said the decision to suspend him had left him “disgusted and in shock”.
He told the Press Association he had been sent a letter announcing he was suspended, pending a hearing.
Draper said the action was taken over something he wrote on social media website Twitter. When approached for comment, the Labour Party said it did not discuss national executive committee (NEC) decisions on individual members.
BFAWU is among those backing Corbyn in his leadership battle against Owen Smith. He has regularly tweeted in support of Corbyn, saying a vote for him was “a vote for progressive, compassionate, working-class policies”.
The suspension comes amid a bitter internal battle within the party connected to the leadership bid, especially over who will be allowed to vote in the forthcoming election.
Last month BFAWU urged the public to boycott Samworth Brothers’ products during a protest in Leicester. The union claimed it had seen a “bullying” letter given to employees at Samworth’s Kettleby Foods site in Melton Mowbray, Leicestershire.