An inkjet printer includes an inkjet printhead and an ink pressure regulator in fluid communication with the printhead via an ink line. The regulator includes an ink chamber having an ink outlet connected to the ink line; an air inlet; a regulator channel having a first end communicating with the air inlet and a second end defining a bubble outlet; and a wetting system for maintaining liquid in the regulator channel. The regulator channel is dimensioned to control a Laplace pressure of air bubbles drawn from the bubble outlet as result of supplying ink to the printhead, thereby regulating a hydrostatic pressure of the ink.