Arthurs, ranked No 364 in the world, defeated Edberg, the world No 3, in a dramatic quarter-final, 7-6, 6-7, 7-6, in 2hr 10min.
Edberg admitted afterwards that he was suffering from a back injury that could place his appearance at Wimbledon in doubt.
It completes a miserable 10 days for Edberg, who was knocked out in the first round of the French Open in Paris, and was hoping to rediscover his form on grass with Wimbledon looming.
Edberg, though, almost won the match. In the third set Edberg led 6-5 and the courageous Arthurs saved no fewer than four match points with booming serves to take the match into a third tie-break.
Arthurs broke Edberg's serve four times and served out to win the tie-break 7-3.
Edberg said: 'I hurt my back this morning, and it's the fourth or fifth time this year. I've played through with it before and got away with it. I took a chance, and it didn't come off.
'I was actually thinking about stopping at one point. I'm only at about 60 per cent fitness at the moment.
'I'm aiming to play next week at the Stella Artois tournament. But if it is not getting any better, I won't play.
Edberg had been expected to be Jeremy Bates's next opponent. The British No 1 progressed into the semi-finals, beating South Africa's Grant Stafford 6-4, 6-1. In the women's event Monique Javer reached the last four to complete a fine day for Britain.Reuse content