Bjorkman failed to qualify for the main draw for only the first time since 1995. The Swede did not compete in last year’s edition.
Bjorkman was beaten 7-6(5), 6-3 in one hour and 19 minutes by Monaco wild card Benjamin Balleret, aged 23, in the second qualifying round.
He will now take his place with partner Max Mirnyi, as top seeds in the main doubles draw, looking to improve on their current ranking of No. 3 in the Stanford ATP Doubles Race.