Begovic has made four appearances for Pompey this season and has been allowed out to gain further first-team experience rather than provide back-up to David James.
He has previously undertaken loan spells at Macclesfield, Bournemouth and Yeovil, and will spend the next three months at Portman Road.
The 22-year-old made his international debut for Bosnia last Saturday as a late substitute in the World Cup qualifier against Estonia, and played for Canada at the Under-20 World Cup in 2007.
Begovic will go into Roy Keane's squad for Saturday's Championship game at home to Swansea and will battle with Richard Wright for the chance to start.
Ipswich have endured a disappointing start to the season and sit bottom of the table after failing to win in their opening 11 games.