Olympic champion Lavillenie cleared 6.16 metres at an indoor meeting in Donetsk on Saturday, surpassing Sergei Bubka's 1993 mark of 6.15.
He immediately went for an attempt at 6.21 metres but fell on the track and suffered a deep cut in his left heel that has ruled him out of the March 7-9 event in Sopot, Poland.
"The decision was made today to pull out of the indoor world championships," Lavillenie, the indoor pole vault world champion, told a news conference in Paris on Monday.
"It's nothing really serious, no bone or ligament has been injured, it's just a big wound that needed 16 stitches. I will take my time to recover well, which means I won't put my foot on the ground for at least two weeks."
The 27-year-old has had a stunning start to the year, beating his personal best twice before eclipsing Bubka in the Ukrainian's hometown.
The Frenchman, who has so far failed to clinch an outdoor world title, believes he will be able to go higher in the years to come with Bubka's outdoor record of 6.14 in his sights.
"Obviously I am thinking a lot about the future because I am still young, I still have the best years and competitions ahead of me and I think I still have a margin for progress," he said.
"It all happened quite quickly this season and I feel there are still things that can be refined."
The Frenchman was surprised by the impact of Saturday's performance.
"I was not expecting this level of congratulations and publicity because I am not used to that," he said.
"I've been compared to a list of champions who belong to another world to me. It's so big that making history is almost scary."