The protesters - wearing 'Just Stop Oil' shirts - invaded the Sheffield stage shortly after play had begun on the evening session of day three.
One male activist managed to jump on top of a table during the first-round match taking place on live television between Robert Milkins and Joe Perry, knocking a couple of balls before unleashing a packet of orange-coloured dye.
A female protester was also stopped from interrupting the match between Mark Allen and Fan Zhengyi after a quick intervention by the referee.
Play was suspended as cleaners looked to clean up the mess ahead of any play continuing.
Seven-time world champion Stephen Hendry, working as a pundit at the event for the BBC, told of his shock at the chaotic scenes: "I have never seen that before at a snooker event. It's a first.
"It is scary. You just hope the cloth can be recovered from that. It caught us all by surprise and then this happens.
"For me, straight away as a snooker player I am thinking: 'Is the table recoverable?' We don't know what that is on the table."
The protestors were reportedly removed from the venue and play resumed after a 45-minute delay.
World Snooker Tour said the vandalised table one would be reclothed overnight and the match rescheduled with the opening session on Tuesday evening and the concluding session on Thursday.
"This is the Crucible. The show will go on," they said on Twitter.
Just Stop Oil named the protesters in a statement on the website as former museum professional Margaret Reid (52) and Exeter University student Eddie Whittingham (25).
Just Stop Oil posted a video of the incident on their Twitter feed with the caption "New oil and gas will snooker us".
The group wants Britain to stop all new oil and gas projects and has staged a number of protests including activists throwing soup over Vincent van Gogh’s painting "Sunflowers" at London's National Gallery last October.
Activists also ran onto the track after an opening lap crash at last July's British Formula One Grand Prix at Silverstone.
