In a statement, the bank said: "Technical issues over the past few days have caused considerable disruption to many of our retail and business customers, as well as customers of other banks. We have made significant progress in resolving the issues and are working around the clock to put things right for our customers.
"Under the circumstances, we felt it would be inappropriate to provide client hospitality at Wimbledon. Our people are focused on resuming normal service for our customers as soon as possible."
RBS had already hosted clients for the first two days of the championships at the All England Club and had planned to do so for the rest of the fortnight.
It declined to say how much it was planning to spend on hospitality and how many people would have attended.
A recent IT meltdown left thousands of RBS customers without access to cash and also affected customers at NatWest and Ulster Bank which are owned by RBS.
It has now updated all but 1% of NatWest and RBS account balances and hopes to restore a full service to Ulster Bank accounts by the start of next week.
Mervyn King, governor of the Bank of England, told MPs there would need to be a detailed investigation into the IT problems.
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