This was announced by the Vatican press office on Thursday, the day the cardinal turned 75.
A successor has not yet been appointed.
The leadership of the archdiocese was temporarily transferred to the bishop of the northern Thai city of Chang Mai, Francis Xavier Vira Arpondratana.
However, according to media reports, the pontiff's quick acceptance of the resignation was not surprising.
As the news agency "AsiaNews" reported, there had been considerable tension between the archbishop and a large part of the clergy for some time. The reason for this is said to be decisions in the leadership of the archdiocese.
The archdiocese of Bangkok currently has just over 122,000 faithful, which corresponds to 0.9 per cent of the predominantly Buddhist population. The local church comprises 59 parishes in which around 240 priests, including diocesan priests, religious and missionary priests, carry out their pastoral work.
Kovithavanij is the second cardinal in the history of the Thai church after his predecessor, Archbishop Emeritus Michael Michai Kitbunchu, who headed the archdiocese from 1972 to 2009.
Kovithavanij was ordained a priest in 1977.
After serving as rector of the National Seminary in Sampran and as a cathedral parish priest, he was appointed Bishop of Nakhon Sawan by Pope Benedict XVI in 2007.
Two years later, he succeeded Cardinal Kitbunchu as Archbishop of Bangkok.
Pope Francis appointed him to the College of Cardinals in 2015.