It was the first time warning shots have been fired in such an incident amid a period of heightened tension between China and Taiwan, which it views as its own territory.
Taiwan strongly disputes China's sovereignty claims.
The drone headed back to China after the shots were fired, a military spokesman said.
Taiwan has complained of Chinese drones repeatedly flying very close to small groups of islands it controls near China's coast, most recently by the Kinmen islands, as part of military drills by China.
China has carried out the exercises around the island after a visit by US House of Representatives Speaker Nancy Pelosi this month.
Kinmen defence command spokesman Chang Jung-shun said the live rounds were fired just before 6pm on Tuesday at the drone which had approached Erdan islet, with flares being used previously.
The drone then flew off back to China, he said.
There was no immediate response from China.
On Monday, the Chinese Foreign Ministry dismissed Taiwan's complaints about the drones as nothing "to make a fuss about".
Footage of at least two drone missions showing Taiwanese soldiers at their posts, and in one case throwing rocks at a drone, have circulated widely on Chinese social media.
Speaking earlier on Tuesday while visiting the armed forces on the Penghu islands, Tsai criticised China for its drone and other "grey zone" warfare activity.
"I want to tell everyone that the more the enemy provokes, the more calm we must be," Tsai told naval officers.
"We will not provoke disputes and we will exercise self-restraint but it does not mean that we will not counter."
She said she had ordered the defence ministry to take "necessary and strong countermeasures" to defend their airspace.
She did not elaborate.
The Kinmen islands are at their closest point just a few hundred metres from Chinese territory, opposite China's Xiamen and Quanzhou cities.
Officers told reporters accompanying Tsai that warships and fighter jets based at Penghu - which lies in the Taiwan Strait closer to Taiwan than China - have been going out armed with live ammunition since China began its exercises this month although they have not opened fire.
Frigate captain Lee Kuang-ping said they had regularly traded radio warnings with Chinese warships.
"Sometimes near the drill zone communist Chinese fishing boats appear, and they provocatively say 'hit them, hit them!'" Lee said.
On a Facebook post citing a navy commander in Penghu, Tsai said ships from both sides came as close as 500-600 metres to each other and Taiwan ships "strictly monitored" their Chinese counterparts.
The Chinese military unit responsible for the area adjacent to Taiwan, the People's Liberation Army's Eastern Theatre Command, released on August 15 a video of the Penghu islands apparently taken by China's air force.
Taiwan's military termed the video information warfare, accusing China of exaggeration and saying it was not true Chinese forces had come near the islands.
Taiwan's armed forces are well-equipped but dwarfed by China's.
Tsai has been overseeing a modernisation program and has made increasing defence spending a priority.
Asked about the Chinese drone activities earlier on Tuesday, Taiwan Defence Minister Chiu Kuo-cheng said he could not give details on what they would do to counter the incursions but he said the military would react based on the principle of "self defence".
"Don't make a fuss then when I set off some firecrackers to scare away some sparrows," he told reporters in Taipei in a veiled warning to China.
