Just Stop Oil protesters ran onto Court 18 during the first-round match between 21st-seed Grigor Dimitrov and Japanese qualifier Sho Shimabukuro.
A man sat down near the net and removed his jacket while a woman was escorted away by officials.
One fan shouted “Get off the court” as spectators booed and jeered.
Play was halted on Court 18 for a second time after another protester threw confetti onto the grass during British number one Katie Boulter’s first-round match against Australia’s Daria Saville.
Just Stop Oil wants the UK government to end all new oil and gas exploration and has promised not to let up in its protests until it does so. The group issued a statement after the first demonstration confirming it was behind the action. “The supporters threw environmentally friendly orange confetti glitter and jigsaw pieces onto the court, before being removed,” it said.
“Play was briefly delayed whilst marshals picked up the pieces.”
Simon Milner-Edwards, 66, who took part in the action, said in the statement: “I’m here for my grandchildren and everybody else’s.
“I’m not prepared to let our politicians wreck everything and leave the next generation to pick up the pieces.”
A spokesman for the All England Club said: “Following an incident on Court 18, two individuals have been arrested on suspicion of aggravated trespass and criminal damage and these individuals have now been removed from the grounds.
“Play on the court was temporarily paused and, following a suspension in play due to a rain delay, play is about to resume.”
The Metropolitan Police said on Twitter that a man and a woman were in custody.
Wimbledon chiefs have tightened security following demonstrations elsewhere in the UK.
Three protesters from Just Stop Oil ran onto the ground during the second Ashes cricket Test at Lord’s last week, sprinkling the group’s trademark orange powder.
There were similar demonstrations during the recent World Snooker Championship and English Premiership rugby final, while the group has also targeted Premier League matches.
Former world number four Tim Henman, who sits on the board of the All England Club, said it was difficult to guarantee protests would not happen.
“You prepare as best you can,” he told the BBC. “Obviously, the challenge when you’ve got 35,000-plus people coming to your grounds and you’ve got 18 fields of play, it’s not easy.
“So it will be important for everyone to understand the facts and where these people have come from but it’s frustrating.
“We’ve had enough disruptions with the weather. To get a disruption like that as well is disappointing.”
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