A military coup in the country earlier this month saw Ms Suu Kyi deposed as State Counsellor of Myanmar and placed under arrest.
Her lawyer said that new police charges brought against her this week could see her held indefinitely without trial.
Mr Johnson said the charges amounted to a human rights violation, tweeting: “New charges against Aung San Suu Kyi fabricated by the Myanmar military are a clear violation of her human rights.
“We stand with the people of Myanmar and will ensure those responsible for this coup are held to account.”
He was joined by foreign secretary Dominic Raab, who repeat the UK’s call for Myanmar’s political leaders to be freed.
Mr Raab said: “The charges against Aung San Suu Kyi are politically motivated, and the latest example of the Myanmar military undermining democratically elected politicians.
“Aung San Suu Kyi and all other elected politicians arbitrarily held must be released immediately. The UK and like-minded nations will not ignore these violations. We will ensure those responsible are held to account.”
It comes after Ms Suu Kyi’s lawyer, Khin Maung Zaw, told reporters after a meeting with a judge in the capital Naypitaw that she had been charged with violating Article 25 of the Natural Disaster Management Law, which has been used to prosecute people who have broken coronavirus restrictions.
She had already been charged with possessing walkie-talkies that were imported without being registered.
The prime minister condemned the coup when it took place on 1 February and criticised the “unlawful imprisonment of civilians” and Ms Suu Kyi.
Mr Johnson said: “the vote of the people must be respected and civilian leaders released.”
Protesters have turned out in droves since the coup was carried out, defying an order banning gatherings of five or more people to demand the return of democracy.
In Mandalay on Monday, soldiers and police violently broke up a demonstration attended by more than 1,000 protesters in front of the Myanmar Economic Bank.
They attacked protesters with catapults and sticks, and local media reported rubber bullets being fired into the crowd, injuring several people. Police were also seen aiming guns into the air amid sounds that resembled gunfire to disperse people.
The military contends there was fraud in last year’s election, which Ms Suu Kyi’s party won in a landslide, and says it will hold power for a year before holding new elections. The state election commission found no evidence to support the claims of fraud.
Additional reporting by PA