The Edinburgh prop, affectionately known as 'Chunk' and a popular player in the dressing room, will be sidelined for between six to eight weeks with the injury he suffered as he was packing down for a scrum.
Jacobsen, 28, will be sorely missed both as a player and as a person according to Hogg, who revealed the front-row forward has also proved quite adept at another sport over the last few weeks.
"He's obviously down and Chunk's a massive part of the squad," said the flanker.
"I really feel for him and he'll be missed, especially on the table tennis table.
"I think he's 10-6 up on Scott MacLeod, so he'll take that as his one achievement of the World Cup!"
Chunk claimed he would be leaving as the "champ", in reference to his table tennis exploits, but there was no hiding his grief at having to leave the squad so early in the tournament.
"We went down and I took a couple of steps forward, felt good and then there was a pop," he said.
"It felt like someone had poked me in the back of the calf. I knew it was something serious.
"The scrum came up, I stood up and as I went to step, my leg just gave way.
"I went to stand up again and I couldn't put any weight on it.
"I pretty much knew what had happened. I went to hospital and they told me I had a hole in the muscle.
"I was kind of hoping I'd be all right, so I am devastated. It is only the beginning but it is already the end."
In two World Cups, Jacobsen has played less than a half an hour of rugby.
In 2003, he was called up during the tournament as an injury replacement but failed to play a part in any of the three games he was in Australia for.
"I want to at least get 80 minutes of World Cup rugby in my career. If it takes three World Cups, then so be it!" he added.