Britain's third biggest drugmaker did not reveal how much it was paying for the Uppsala-based business but said it would pay a sum upfront followed by contingent payments based on clinical development and commercial success.
The acquisition takes Shire into the new area of neonatology - the treatment of sick or premature newborn infants - and expands its already substantial presence in rare diseases.
Treating diseases that affect only a small number of patients is a growing focus for many drug companies given the high prices that can be achieved.
Premacure, which was launched in 2006, has an experimental protein replacement medicine in mid-stage Phase II clinical development for the prevention of retinopathy of prematurity (ROP).
Normal full-term babies produce enough growth factors on their own to prevent diseases like ROP. But those born before 31 weeks may lack chemicals such as insulin-like growth factor 1 (IGF-1), which can result in life-long complications like ROP.
Shire said its human genetic therapies unit would continue with the Phase II study, the primary goal of which is to restore the IGF-1 levels in premature infants to those found in babies born at full term.
(Reporting by Ben Hirschler; Editing by Greg Mahlich)