The loss of the Edinburgh forward for the remainder of the Six Nations is a major blow to head coach Frank Hadden.
Jacobsen, 30, played in all 10 of Scotland‘s internationals in 2008 and has also been ever-present in the tournament so far.
Hadden received better news on lock Alastair Kellock and centre Max Evans. Kellock, who was recalled in the absence of the injured Nathan Hines and Jim Hamilton, strained ankle ligaments during the Scots 26-6 victory over Italy on Saturday but he will be fit for the visit of Ireland on March 14.
There were fears Glasgow team-mate Evans had suffered a fractured cheekbone but X-ray results allayed those.
Winger Simon Danielli is ready and able to offer the Scotland squad some inside knowledge of his Ulster team-mates in the Ireland set-up.
He added: “I think anyone who plays in the Magners League will know of their new players but I will certainly be able to pass on information about the Ulster players such as Stevie Ferris, Paddy Wallace and Rory Best.
“They’ve played well in the Six Nations and came through an intense affair against England on Saturday.”
SCOTLAND: Southwell, Danielli, M. Evans, Morrison, T. Evans, Godman, Barclay, Blair, Jacobsen, Ford, Murray, White, Kellock, Strokosch, Taylor.
Replacements: Paterson for Southwell (47), De Luca for Morrison (67), Gray for Barclay (56), Cusiter for Blair (55), Brown for Jacobsen (68), Hall for Ford (53), Dickinson for Murray (67).
ITALY: Marcato, M. Bergamasco, Canale, Garcia, Pratichetti, McLean, Griffen, Perugini, Ghiraldini, Castrogiovanni, Dellape, Bortolami, Zanni, M. Bergamasco, Parisse.
Replacements: Rubini for Marcato (47), Bacchetti for Garcia (3), Canavosio for Griffen (55), Sbaraglini for Ghiraldini (58), Nieto for Castrogiovanni (58), Del Fava for Dellape (57), Sole for Bortolami (77).