A spokesperson told Rene Ritchie:
We are sorry that some of our users are receiving spam calendar invitations. We are actively working to address this issue by identifying and blocking suspicious senders and spam in the invites being sent.
Unfortunately, you currently cannot mark calendar invitations as spam and responding to the invitation will only confirm your email address is valid to the spammer.
The best solution at this time appears to be logging into iCloud.com, selecting Calendar, navigating to Settings, and sending your invites to email. You can then delete the email invite. Alternatively, a second calendar can be created and you can move the invite to that calendar then delete the entire calendar without the spammer being notified.
We'll let you know if Apple takes any further steps to address the issue. Please follow iClarified on Twitter, Facebook, Google+, or RSS for updates.