Minetta Brook originally flowed into a marshy region that is now Washington Square Park. (Some brief information on the Parks Department site at http://www.nycgovparks.org/parks/washingtonsquarepark/).
A schematic of Washington Square Park from the parks department; this shows planned renovations, including moving the fountain slightly to bring it into line with the Arch, but is very close to the plan of the park as it exists today.
Washington Square Park does not have any obvious signs of the old watercourse. Between the development of the park and the real estate development around it in the 19th century, it's been changed many times from its original form. However the water still has to go somewhere, and today there are three parallel combined sewers (carrying both drainage water and sewage) running east to west: one on the north side of the park (Waverly Place/Washington Square North), in a pipe 4'2" by 4"; another on the south side of the park (West 4th St), 4' by 3'; and one through the middle of the park, with a diameter of 54" (4.5 feet). These are shown on the sewer diagram below; probably all three are brick tunnels, from mid- to late-nineteenth century construction. Which, if any of these, carries the remnants of the Minetta Brook?