This figure represents an increase on last year's 1.3 million parcels per day.
Experts say this is due to the growing popularity of online shopping.
With 8.4 million people living in Switzerland, this means that 1 in 6 citizens had a parcel delivered during the last week before Christmas.
But despite the busiest time coming in the week before Christmas, Swiss Post also sorted through 1 million packages a day in the weeks beforehand.
Since Black Friday, on November 23, Swiss Post says it has delivered some 25 million parcels and more than 400 million letters.
To compensate for the sudden spike, all available staff in three of the biggest Swiss Post sorting centres (Frauenfeld in Thurgau, Härkigen in Solothurn and Daillens in Vaud) have been working extra shifts on Saturdays for the last five weeks.
Swiss Post has expanded its sorting system in the past few years to further help it cope with such high numbers of parcels.
It is also currently working on the construction of three new regional sorting centres in Ticino, Valais and Graubünden.