The long-serving prop, who has made 195 appearances for the club over a nine-year period, damaged his groin while on RBS 6 Nations duty with Scotland.
As a result, the fans' favourite has been ruled out for the return match against Glasgow with Edinburgh in pole position to lifting the trophy after winning the previous encounter 35-31 in late December.
Jacobsen said: "I'm absolutely gutted to be missing the match at Glasgow. There is always something extra about the game when we play against Glasgow; it is a real derby match.
"All the boys get really up for it and the Cup we are playing for adds a bit extra to the occasion as well. Although I won't be out on the pitch, I will be cheering the boys on from the stands and I think there will be a special atmosphere at the game."
Born in Edinburgh and raised in Prestonpans, Jacobsen has got such a strong affinity for the area that when he was handed a week's break headed to North Berwick rather than experience an overseas holiday.
The 29-year-old says he has developed an unbreakable bond with Edinburgh and its supporters and cannot ever envisage himself playing for another team.
He added: "It means a lot to me to wear the black and red of Edinburgh. I came here when I was a boy; I played all my age group rugby for Edinburgh and then worked my way up through the ranks.
"I have played with a lot of good players here at the club and I have made a lot of friends. I'm just really proud to play for the club and feel a massive amount of loyalty for Edinburgh. You never know what is around the corner, but I would like to play here for as long as I can."
Jacobsen featured in the previous meeting between the two sides in late December when Edinburgh fought back to clinch a 35-31 victory by scoring a try with only minutes remaining.
The Scotland internationalist remembers the feeling of elation in the aftermath of the result and believes it triggered off a run of results that saw both Cardiff and Leicester defeated in the following two matches.
He said: "We had led the whole game and then we went behind. Glasgow were playing some good stuff, but the boys showed a lot of spirit to come back and win it with the last move of the match. That result gave us the confidence that helped us to win against Cardiff and Leicester."
Even though he is unable to play, Jacobsen is planning to be part of the huge contingent of Edinburgh fans set to travel west to Firhill Arena.
He said: "It would be great if we could take a lot of support over to Firhill for the match. When we won at Ulster for the first time in ages it was really good to be able to share that with the supporters who had travelled over to the game.
"Playing away games in different countries means that sometimes it is difficult for our fans to come and watch us. So it is excellent that the club are providing coaches for such good prices (£5 for travel from Murrayfield to Firhill Arena) so that our fans can come and cheer us on."
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