Mr Trump, who has faced a barrage of controversy since a video emerged of him talking about groping women, said Mrs Clinton had been “pumped up” during their last debate.
On the campaign trail in New Hampshire, Mr Trump said that while Mrs Clinton had been “all pumped up” at the start of their last televised debate, she was struggling to reach her car when it finished.
“We should take a drugs test,” he added without providing any evidence at all to back up his claims.
It is the latest in a series of comments Mr Trump has made about Mrs Clinton’s “strength and stamina” which began when the Democrat candidate suffered from a bout of pneumonia.
Mr Trump said that presidential candidates prepared like athletes for their campaign. “Athletes, they make them take a drug test. I think we should take a drug test prior to the debate,” he said. “I’m willing to do it.”
He has been making an increasingly far-fetched string of allegations as he seeks to deflect attention away from accusations from a number of women that Mr Trump has touched them inappropriately.
Not only did he hint that Mrs Clinton was taking medication of some sort, he also said that the election was rigged and that a global media conspiracy was trying to stop him from taking office.
Meanwhile, Mrs Clinton’s camp is said to be sensing victory and is taking the strategy of letting Mr Trump shoot himself in the foot.
William Galston, a former adviser to Bill Clinton, said: “There’s an old principle. When your opponent is hanging himself, get out of the way. The Clinton campaign is adhering to that principle.”
While Trump has criticised her for laying low, Mrs Clinton is said to be leaving others to sing her praises while she prepares for the next debate.
Instead, powerful Democrats have been travelling the US to shout about why Mrs Clinton should be the next American president. Bill Clinton, Barack Obama, Michelle Obama, vice-president Joe Biden and senators Bernie Sanders and Elizabeth Warren have all been part of the campaign trail.
Mr Galston added: “In a media frenzy such as this one, there just isn’t room for a second narrative and if you pop your head up you’re part of that story whether you want to be or not.”