It is believed the bikes were driven onto Notts. Golf Club, also known as Hollinwell, on Sunday afternoon.
Members have estimated there are "ditches" up to nine inches (23cm) deep across the green.
Captain Stewart England said the course - one of the top 100 in England - has had issues with bikes for a long time.
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"Two motorbikes, we think, went onto [the] golf course and totally wrecked it," Mr England said. "It's really badly damaged and will cost tens of thousands of pounds to put right.
"The green has - what I would only term as ditches, created by motorcycle rear wheels being spun at such a speed that they've dug into the ground about eight or nine inches.
"It has to be seen to be believed really, the amount of mindless damage that's been caused."
Mr England said the damaged area would be out of action for "probably months".
"It's ranked amongst the top courses and people come from all over the world to play it," Mr England said. "It really is a shame that people can do this sort of damage without any thought."
A Nottinghamshire Police spokesman said: "This matter has been reported to us and we are liaising with the owners of the golf course."
Anyone with any information on the vandalism is asked to contact the force.
Motorbikes have caused damage which will cost "thousands of pounds" to repair at one of Nottinghamshire's most famous golf courses.