A man was detained at the scene in Wakayama, where Mr Kishida had been due to give a speech, local media reported.
A witness said they saw a person throwing something, followed by smoke, while another said they heard a big bang. No injuries were reported.
Video showed officers piling on top of a person, believed to be a suspect.
He was arrested on suspicion of obstruction of business and later identified by the authorities as 24-year-old Ryuji Kimura. His motivation is still unclear.
Japan’s public broadcaster, NHK, quoted Mr Kishida as saying there was a “loud blast” at the venue. “Police are investigating details, but I’d like to apologise for worrying many people and causing them trouble.
NHK broadcast footage in which crowds of people appear to be running away from the scene.
The footage also shows people swarm around one man, hold him down, and then carry him away.
Mr Kishida had just started to deliver a speech after touring the fishing harbour in Wakayama for a campaign event when the object was thrown and he took cover.
After the incident, Mr Kishida addressed a crowd in another location and said the incident should not disrupt the electoral process.
A woman at the scene told NHK: “I was stunned. My heart is still beating fast.”
A person who said they saw an object flying through the air said it gave them a “bad feeling, so we ran away unbelievably fast”.
“Then we heard a really loud noise. It made my daughter cry,” they added.
Another witness told NHK that the crowd began to disperse in panic before the blast was heard, as someone said an explosive had been thrown.
Hiroshi Moriyama, a member of Mr Kishida’s Liberal Democratic Party, said: “That something like this happened in the middle of an election campaign that constitutes the foundation of democracy is regrettable. It’s an unforgivable atrocity.”
Violent attacks are extremely rare in Japan. But there is nervousness about security around politicians, after former Prime Minister Shinzo Abe was shot dead while on the campaign trail last year.
Source: BBC