The Prime Minister condemned the atrocity as she called on Russia to ensure Bashar Assad's regime is brought to an end.
Opposition activists claim that dozens of people died in the attack in a town in the northern province of Idlib, with the British-based Syrian Observatory for Human Rights putting the death toll at 58, including 11 children.
Mrs May said: "I'm appalled by the reports that there's been a chemical weapons attack on a town south of Idlib allegedly by the Syrian regime.
"We condemn the use of chemical weapons in all circumstances.
"If proven, this will be further evidence of the barbarism of the Syrian regime, and the UK has led international efforts to call to account the Syrian regime and Daesh for the use of chemical weapons and I would urge the Organisation for the Prohibition of Chemical Weapons to investigate this incident as soon as possible.
"I'm very clear that there can be no future for Assad in a stable Syria which is representative of all the Syrian people and I call on all the third parties involved to ensure that we have a transition away from Assad.
"We cannot allow this suffering to continue."
Earlier, Foreign Secretary Boris Johnson denounced the attack as a "war crime" and called for those responsible to be brought to justice.
It would be "unbelievable" to think that president Bashar Assad could play a role in the post-war government of the country if his regime is found to be to blame, Mr Johnson said.
It was the third claim of a chemical attack in just over a week in Syria. There was no immediate comment from the government in Damascus on the alleged incident, which comes a day before a conference on the future of Syria co-hosted by Britain in Brussels.
Speaking in London, Mr Johnson - who will represent the UK at Wednesday's summit - said: "If this were proved to have been committed by the Assad regime, it would be another reason to think they are an absolutely heinous outfit.
"Bombing your own civilians with chemical weapons is unquestionably a war crime and they must be held to account.
"It is unbelievable to think that in the long term, Bashar Assad can play a part in the future of Syria, given what he has done to his people."
France's foreign minister Jean-Marc Ayrault called for an emergency United Nations Security Council meeting to discuss the "atrocious act".
The Syrian activists had no information on what agent could have been used in the assault on the town of Khan Sheikhoun, which they blamed on an air strike carried out either by the Syrian government or Russian warplanes.
Idlib province is largely opposition-controlled and is home to around 900,000 Syrians displaced from their homes elsewhere in the country.
Labour's shadow foreign secretary Emily Thornberry said: "This was a shocking and barbaric attack, and our thoughts are with all the victims and their loved ones."
The UN Security Council will hold an emergency meeting at 3pm UK time on Wednesday to discuss the reports from Idlib in Syria of chemical attacks. This meeting is at the request of the UK and France.