Chinese targets have regularly been attacked by separatists from Balochistan, where Beijing is involved in huge infrastructure projects as part of its Belt and Road Initiative.
Separatists have long harboured resentment against lucrative mining and energy projects in the region, saying locals do not see the benefits and are being pushed off their land.
The "Baloch Liberation Army accepts responsibility of today's self-sacrificing attack", the group's spokesman, Jeeyand Baloch, said in a statement published in English on Telegram.
Karachi police confirmed four people had died, including the minibus driver and three staff from the Confucius Institute, the cultural and educational program that China operates at universities around the world.
CCTV footage broadcast by local channels showed a woman standing near the gate of the institute, inside the Karachi University grounds, as the minibus pulls up.
When it gets to within a metre she turns her back on it and detonates a bomb strapped to her body. Pakistan's new Prime Minister Shehbaz Sharif immediately condemned the attack. "I am deeply grieved on the loss of precious lives including of our Chinese friends in the heinous attack in Karachi today," he tweeted.
Sharif only took over as premier after Imran Khan was ousted by a no-confidence vote earlier this month, and tackling a resurgence in militancy will be one of his biggest challenges.
"I strongly condemn this cowardly act of terrorism," Sharif said, adding "the perpetrators will surely be brought to justice".
In February, Baloch separatists staged four days of attacks across two locations in the province, killing nine soldiers.
Tensions have flared in recent years in Balochistan following a massive influx of Chinese investment.
China is upgrading energy links and infrastructure as part of a $54 billion programme known as the China-Pakistan Economic Corridor, with both nations wary of security threats to the projects.
In April 2021 a suicide bomb attack at a luxury hotel hosting the Chinese ambassador in Quetta, the provincial capital of Balochistan, killed four and wounded dozens.
The ambassador was unhurt.