The young Swede, who made his breakthrough this year and is ranked 125th in the world, made it to the main tournament after winning the qualifying final.
But in the first round, she encountered really tough opposition in the newly formed world runner-up Ons Jabeur, Tunisia - and was without a chance.
The match was over after 54 minutes of play and 2-0 in sets.
It was Björklund's second grand slam tournament.
Also in the French Open earlier this summer, she went out immediately.