The 21-year-old striker, who has 13 caps for the All Whites, has only managed one first-team appearance for the Tractor Boys this term.
Auckland-born Patterson joined Ipswich in 2013 and has come through the club's academy, making his debut in the cup this season.
Patterson joins a Wellington side who are currently bottom of the A-League ladder.
Phoenix have managed 22 goals in 17 matches this term, with Andrija Kaluderovic (eight goals) and Roy Krishna (four goals) their top scorers.
Wellington also signed Nathan Burns and Matija Ljujic during January, with Dario Vidosic leaving for Melbourne City, along with Ali Abbas, Hamish Watson, Luke Tongue and Liam Wood.
Patterson's contract at Ipswich expires at the end of this season.