The measure means intelligence and security agencies have concluded another attack may be imminent.
May said: “For this period, military personnel will replace police officers on guard duties at certain protected sites that are not accessible to the public.”
Just before the announcement Islamic State claimed responsibility for the attack.
Assistant Commissioner Mark Rowley said police were “chasing down suspects”.
He added: “Communities across the UK can expect to see more officers, both armed and unarmed, on patrol by foot and in vehicles over the weekend. In particular, they will be patrolling at crowded places, iconic sites, transport hubs and ports.
“This may mean disruption for those who are travelling. The public are asked to be patient and plan ahead, allowing time for delays.
“Police are reviewing the security of events across the UK and working with businesses and organisers to make events as secure as possible.
“Security checks at events will be enhanced, so people attending events should arrive early and allow extra time for these checks. If you don’t need to take a bag, don’t take it.”
The home-made bomb on a packed rush-hour commuter train in London engulfed a carriage in flames and injured 29 people on Friday in the UK’s fifth major terrorism incident this year, but apparently failed to fully explode.
Passengers heading into the British capital fled in panic after the blast as the train was about to depart Parsons Green underground station in West London at 8.20am.
Some suffered burns and others were injured in a stampede to escape but health officials said none were thought to be in a serious condition.
“We now assess that this was a detonation of an improvised explosive device,” Britain’s top counter-terrorism officer Mark Rowley told reporters.
Police said a hunt involving hundreds of detectives backed by the intelligence services was underway to find out who was responsible.
Rowley declined to say if the suspected bomber had been on the train, saying it was a live investigation.
Pictures taken at the scene showed a slightly-charred white bucket with a supermarket freezer bag on the floor of one train carriage. The bucket, still intact, was in flames and there appeared to be wires coming out of the top.
“I was on second carriage from the back. I just heard a kind of whoosh. I looked up and saw the whole carriage engulfed in flames making its way toward me,” Ola Fayankinnu, who was on the train, told Reuters.
“There were phones, hats, bags all over the place and when I looked back I saw a bag with flames.”
Charlie Craven said he had just got on the train when the device exploded.
“Literally within three seconds of putting your bag down, the doors just closing, we hear a loud explosion,” he told Reuters. “I looked around and saw this massive fireball … coming down the carriage.”
He said terrified passengers fled, fearing a second explosion or a gunman, with people being knocked to the ground and crushed in the stampede to escape.
Outside the station, a woman was carried off on a stretcher with her legs covered in a foil blanket while others were led away swathed in bandages. Health officials said 29 were taken to hospital most suffering from flash burns.