Arthurs, 36, had been contemplating going back on his decision to retire at the end of the tournament if he reached the quarter-finals at the All-England Club.
But Björkman, 35, produced a ruthless display to inflict a 6-2, 6-1, 6-4 defeat that is likely to herald the end of the Australian’s career, as he set up a fourth round meeting with seventh seed Tomas Berdych.
With a combined age of 71 it would have been no surprise to hear a few creaking bones as Björkman and Arthurs battled it out.
But Björkman, the 19th seed, had no reason to fear that age would hinder him. After all in 2006 he had become Wimbledon’s oldest semi-finalist for 19 years and he was able to dismiss his fellow veteran with ease.
Arthurs was presented with a wheelchair by Wimbledon changing room assistants in joking tribute to his victory over world number seven Tommy Robredo in the previous round.
But the exertions of playing three qualifying matches and then going straight into a Grand Slam finally seemed to have caught up with him.
If he does hang up his racket he would have preferred to have gone out with a more dynamic display than this.
Björkman broke in the fourth game and raced away with the first set.
Arthurs struggled to find his usual serve and volley rhythm and was broken again early in the second set as the Swede moved in for the kill.
Rain early in the third set offered Arthurs a chance to regroup, but Björkman broke immediately after the re-start and easily held serve to close out the tie.