The off-spinner reached the landmark when he had Bangladesh's last man Syed Rasel caught in the deep by Farveez Maharoof on the fourth day of the third and final cricket Test at the Asgiriya stadium here.
The dismissal signalled Sri Lanka's victory by an innings and 193 runs to give the hosts a 3-0 sweep of the series.
Muralitharan finished with six wickets in each innings to claim 10 wickets or more in a Test for the 20th time.
Muralitharan, 35, is now just nine wickets away from surpassing the retired Warne's world record tally of 708.
Sri Lanka are due to tour Australia for two Test matches in November, but Muralitharan was unsure of becoming the leading bowler in Warne's backyard.
"The record will come sometime in the near future, but I am not sure it will happen in Australia because the wickets there usually help fast bowlers," he said.
"I don't know how much I will get to bowl in Australia because our fast bowlers could grab most of the wickets.
"But I am just delighted to get to 700 in Kandy which is my home town. I can't ask for more."
Muralitharan, a veteran of 113 Tests who made his debut against Australia in 1992, said he had worked hard over the last 15 years to become one of the most feared bowlers in the game.
"So many years at the top takes a lot out of you but I am still hungry for wickets and that is what matters."
The off-spinner was controversially called for throwing by Australian umpire Darrell Hair during Sri Lanka's tour Down Under in 1995.
Two years later, another Australian umpire, Ross Emerson, called Muralitharan during a one-day series there, prompting a bio-mechanical analysis of his bowling action at the University of Western Australia in Perth.
The International Cricket Council cleared Muralitharan and his bowling action has not been questioned any more by umpires around the world.