Koepka took a two-shot lead into the delayed third round and had doubled his advantage over Jon Rahm in the space of just five holes as greenkeeping staff battled to remove standing water from a number of greens.
The final group had reached the seventh green by the time play was called off at 3.15pm local time, with Koepka on 13 under par and Rahm nine under.
US Amateur champion Sam Bennett was three strokes further back, with Matt Fitzpatrick, Patrick Cantlay, Viktor Hovland and Collin Morikawa all on five under.
At the other end of the leaderboard, Tiger Woods had slumped to last place of the 54 players to make the cut after covering his first seven holes in six over par.
Koepka and Rahm had both made birdie on the par-five second when the third round got under way, but Rahm bogeyed the fourth after a wayward tee shot and then three-putted the next from long range.
“Obviously when we walked up to the seventh green it was clear to us that it had been wet for a while,” Rahm said.
“I understand they’re trying to push us to play as many holes as possible, but it was very apparent when they tried to get the water out that it just wasn’t going to happen in our case.
“You can’t really say it was (too) late because I don’t blame them for wanting us to play as much as possible. It was just too bad I couldn’t save at least one par on four or five, but I made a great swing on six and two great swings on seven.
“So I’m feeling confident, playing good golf and there’s a lot to be played.”
Koepka, who won four majors in eight starts and also finished runner-up to Woods in the 2019 Masters in that stretch, added: “I’m not too concerned about playing 29 holes or however many holes we’ve got left. It’s part of the deal.
“I’m pretty sure I’ll be up for it considering it is the Masters. So I don’t think anybody should have a problem with that.”
Woods had endured a miserable afternoon, dropping shots on the 10th and 14th before carding consecutive double bogeys on the 15th and 16th.
It was the first time in his career that Woods had made a double bogey on the par-three 16th and also the first time that he had recorded back-to-back double bogeys.
Woods had earlier enjoyed a little unintentional help from his friends as he made a record-equalling 23rd consecutive cut in the Masters.
The 15-time major winner had seven holes of his second round to complete when play resumed at 8am and followed three pars with a birdie on the 15th to get inside the projected cut mark.
However, dropped shots on the 17th and 18th left Woods on three over par and needing help from elsewhere to join Gary Player (1959-82) and Fred Couples (1983-2007) in the record books.
That assistance immediately arrived as good friend Justin Thomas badly hooked his tee shot on the 17th and went on to bogey the hole, dropping to three over himself and moving the cut to the same score.
Thomas also bogeyed the 18th to miss the cut as 54 players qualified for the last 36 holes on three over.
Speaking before the cut had been confirmed, Woods said: “I’ve always loved this golf course and I love playing this event. Obviously I’ve missed a couple with some injuries, but I’ve always wanted to play here.
“I hope I get a chance to play this weekend. I wish I get a chance to play two more rounds.”
Rahm had reached nine under par midway through his round when play was suspended for the second time on Friday afternoon as strong winds brought three trees crashing down across the 17th tee, remarkably not injuring any spectators.
The world number three twice closed to within a shot of Koepka thanks to birdies on the 12th, 15th and 17th, but bogeys on the 16th and 18th meant he would start round three two behind.
“With the temperature we had and how long the golf course was playing, I was very happy to be able to play the back nine under par,” Rahm told ESPN after adding a 69 to his opening 65.
“The 18th was brutally difficult.”
During the third round, tournament officials had announced a record prize fund of 18million US dollars (£14.49million), an increase of 20 per cent from last year, with the winner pocketing £2.6million.
