UPDATE: Former prime minister Shinzo Abe has died. Read the latest here.
The United States said it was "saddened and shocked" by the incident, said US ambassador Rahm Emanuel.
Japan's longest-serving prime minister was taken to hospital bleeding after being shot while delivering a speech in the western city of Nara days before an upper house election, according to authorities and media.
"Abe-san has been an outstanding leader of Japan and unwavering ally of the US," Emanuel said in a statement.
"The US government and American people are praying for the well-being of Abe-san, his family, and the people of Japan."
Ahead of his meeting with Indonesia's Foreign Minister Retno Marsudi, US Secretary of State Antony Blinken said they are "deeply saddened and deeply concerned" by the news.
"We don't know his condition, we do know he's been shot and our thoughts and prayers are with him and his family, with the people of Japan," he added. "This is a very, very sad moment and we're waiting news from Japan."
Australia's Prime Minister Anthony Albanese said in a tweet that "(their) thoughts are with his family and the people of Japan at this time".
Taiwanese President Tsai Ing-wen said she believes "everyone is as surprised and sad as (she is)" about the incident.
"On behalf of my government, I would like to severely condemn violent and illegal acts," she said.
"Former Prime Minister Abe is not only a good friend of mine, but also a staunch friend of Taiwan's. He has supported Taiwan for many years and spared no effort to promote the progress of Taiwan-Japan relations."
An Indonesian foreign ministry spokesman said in a statement, on behalf of the foreign minister, that she has "expressed her sympathies in the name of G20 foreign ministers to the Japanese foreign minister".
Japan's former Olympics minister Yoshitaka Sakurada, arriving at the Liberal Democratic Party (LDP) headquarters in Tokyo, said: "I can't believe that something like this could happen in the 21st century.
"There's still Russia, that was beyond expectations as well, but I can't believe something like this could happen in Japan."
New Zealand Prime Minister Jacinda Ardern said in a statement that she was "deeply shocked" to hear the news of Abe's shooting.
"He was one of the first leaders I formally met when I became Prime Minister," she said.
"He was deeply committed to his role, and also generous and kind. I recall him asking after the recent loss of our pet when I met him, a small gesture but one that speaks to the kind of person he is.
"My thoughts are with his wife and the people of Japan. Events like this shake us all to the core."
UK Prime Minister Boris Johnson said he was "utterly appalled and saddened to hear about the despicable attack on Shinzo Abe".
"My thoughts are with his family and loved ones," he added.
Calling Abe a "dear friend", India's Prime Minister Narendra Modi said on Twitter that he was "deeply distressed by the attack".
"Our thoughts and prayers are with him, his family, and the people of Japan."
In a statement, Malaysia's Foreign Minister Saifuddin Abdullah said he is "saddened and shocked by the tragic shooting of former Japanese Prime Minister Shinzo Abe".
"The government and people of Malaysia are praying for his speedy recovery and for his family to be given strength to endure this tragedy," he added.