There were gasps from the crowd as the man interrupted Monday's match between Robert Milkins and Joe Perry.
Another protester tried to glue herself to the table where Mark Allen and Fan Zhengyi were playing but was stopped by referee Olivier Marteel.
A man and a woman were later arrested by South Yorkshire Police.
Milkins and Perry's game was abandoned and will resume at 19:00 BST on Tuesday, while Allen and Fan re-started after a 40-minute break.
The protesters both wore T-shirts apparently in support of the group of climate change activists Just Stop Oil, who subsequently posted online to claim responsibility for the disruption to the event.
Milkins and Perry were on table one at the Crucible when a man entered the playing area, jumped and knelt on the table before emptying a bag of orange powder over it.
At the same time on the table next door, a woman attempted to glue herself to the table, but was stopped by Marteel, only managing to grab hold of the middle pocket.
Marteel prevented the woman from accessing the table before security arrived and carried both protesters away.
Staff then began to clean up, with master of ceremonies Rob Walker seen hoovering the table in a bid to try and get their match back under way as quickly as possible.
While play resumed in the Allen v Fan match, the other table was covered and will be re-clothed overnight with the second session of Milkins and Perry's meeting - which was originally due on Tuesday - rescheduled for Thursday from 09:30 BST.
Just Stop Oil have disrupted a number of sporting events, with some individuals attempting to tie themselves to goalposts during Premier League matches.
Yorkshire Police said they had arrested a 30-year-old man and a 52-year-old woman on suspicion of criminal damage over the incident.
After the conclusion of his 10-5 win over Fan, UK Champion Allen told BBC Sport: "I think I was the last person in the whole arena to work out what was going on because I was focused on the shot I was about to play.
"I heard a bang, that I thought it was on the other table and then I turned round and there was a woman on my table.
"It could have been a lot worse - you saw what happened on the other table and how much disruption it caused.
"It was a surreal moment but I feel like even talking about it is giving them airtime they don't deserve because they are just idiots. What are they trying to gain from what they have done? I am sure there are better ways to get their point across."
Speaking on the BBC Red Button, at the time of the incident, seven-time world champion Stephen Hendry said: "I have never seen that before at a snooker event. It's a first.
"It is scary. Wow! 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."