The England Under-18 international has been brought in to cover for Tim Deasy who is undergoing minor knee surgery in Newcastle.
The former Barrow keeper is expected to be sidelined for at least four weeks.
Alnwick, the younger brother of Tottenham Hotspur goalkeeper Ben, was originally with Sunderland.
The Hexham-born keeper played a major role in helping Newcastle United's U.18 side reach the FA Youth Cup semi-finals in 2009/10.
Gateshead boss Ian Bogie: "We have a good relationship with my former club Newcastle and we are grateful that they have allowed Jak Alnwick to join us on loan.
"He is a highly rated young goalkeeper who will deputise for Tim Deasy while he recovers from his operation and it is a deal that benefits all parties."