Armed men pretending to be policemen kidnapped the two language teachers in the provincial capital, Quetta, on May 24. The kidnapping was a rare security incident involving Chinese nationals in Pakistan, where Beijing has pledged $57 billion for its "Belt and Road" plan.
"Islamic State fighters killed two Chinese people they had been holding in Baluchistan province, southwest Pakistan," Amaq said.
A Baluchistan government spokesman said officials were in the process of confirming "whether the report is true".
China's embassy in Pakistan could not be reached and there was no immediate comment from Pakistan's interior ministry or its foreign office.
Islamic State, which controls some territory in neighbouring Afghanistan, has struggled to establish a presence in Pakistan. But it has claimed several major attacks, including one on the deputy chairman of the Senate last month in Baluchistan, in which 25 people were killed.
Earlier on Thursday, Pakistan's military published details of a three-day raid on an militant hideout in a cave not far from Quetta, saying it had killed 12 "hardcore terrorists" from a banned local Islamist group and prevented Islamic State from gaining a "foothold" in Baluchistan.
China's ambassador to Pakistan and other officials have often urged Islamabad to improve security, especially in Baluchistan, where China is building a new port and funding roads to link its western regions with the Arabian Sea.