The provisional reading was measured at the Basel/Binningen station at 1:30 pm (1130 GMT), the Swiss national weather service MeteoSwiss said.
That broke Switzerland's previous June heat record of 38.8C, set at the same station a day earlier, which had passed the 38C-record set there on Thursday.
Before the current heatwave, which has begun moving eastward after roasting much of Western Europe for the past week, Switzerland's June heat record had stood at 36.9C for nearly 80 years.
The 39C measured Saturday was also the hottest temperature ever registered at the Basel station in any month since measurements began in 1897, MeteoSwiss said.
More than a dozen other Swiss cities also broke their all-time heat records Saturday, according to an overview sent by MeteoSwiss to AFP.
Among them was Switzerland's largest city Zurich, where 37.1C was measured, breaking a previous record set in August 2003 of 36C.
The hottest temperature ever measured in Switzerland was 41.5C, registered in Grono, in Graubunden canton in the south, on August 11, 2003, according to MeteoSwiss.
It has said it expects the heatwave in Switzerland to begin subsiding on Monday.
A number of other countries have been crushing records in recent days amid the deadly heatwave sweeping Europe.
AFP analysis suggested almost 200 million would face temperatures of more than 35C on Saturday as an unprecedented hot spell that has already seen records tumble in Britain, France and Denmark.
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