The spacecraft will deliver a crew of three to the Tiangong space station, according to the report.
The Long March 2F carrier rocket took off as scheduled at 9:31 a.m. Beijing time (0131a.m. GMT).
After the launch of Shenzhou 16, the number of people simultaneously in Earth's orbit has reached 17, breaking the previous record of 14 people, set in 2021.
Three cosmonauts are flying to the Tiangong space station, where three others are already working. Eleven people, including Russian cosmonauts and US astronauts, are currently working on the International Space Station (ISS).
China says the Tiangong space station will be the first open to all UN member states and says science experiments from eleven different countries will be conducted on it.