Four players, Terence Atmane, Tristan Boyer, Gustavo Heide and Thiago Seyboth Wild, will have to pay around £3,000 for “unsportsmanlike conduct”.
Kazakhstan’s Denis Yevseyev will have to pay £1,500, while Switzerland’s Alexander Ritschard was fined the same amount for “abuse of rackets and equipment”.
Clare Balding, who is hosting BBC’s Wimbledon coverage, said Draper had made a “sensible” decision in hitting his bag.
She added: “Plenty of times in the past, John McEnroe among others has demanded more passion, particularly from British players.
“Well there’s no doubt Draper has plenty of that, smashing the racket there onto his bag, which is quite sensible because you get fined if you damage the grass.
“If you damage yourself or damage your own kit then that is – albeit I guess it can be painful – not going to earn you a fine.”