We present results of recent Neutron Star Interior Composition Explorer (NICER) observations of the accreting millisecond X-ray pulsar (AMXP) IGR J17062−6143 that show that it resides in a circular, ultracompact binary with a 38-minute orbital period. NICER observed the source for 26 ks over a 5.3-day span in 2017 August, and again for 14 and 11 ks in 2017 October and November, respectively. A power spectral analysis of the August exposure confirms the previous detection of pulsations at 163.656 Hz in Rossi X-ray Timing Explorer (RXTE) data, and reveals phase modulation due to orbital motion of the neutron star. A coherent search for the orbital solution using the Z2 method finds a best-fitting circular orbit with a period of 2278.21 s (37.97 minutes), a projected semimajor axis of 0.00390 lt-s, and a barycentric pulsar frequency of 163.6561105 Hz. This is currently the shortest known orbital period for an AMXP. The mass function is 9.12 × 10−8 M , presently the smallest known for a stellar binary. The minimum donor mass ranges from 0.005 to 0.007 M for a neutron star mass from 1.2 to 2 M . Assuming mass transfer is driven by gravitational radiation, we find donor mass and binary inclination bounds of 0.0175-0.0155 M and 19° < i < 27 5, where the lower and upper bounds correspond to 1.4 and 2 M neutron stars, respectively. Folding the data accounting for the orbital modulation reveals a sinusoidal profile with fractional amplitude 2.04 0.11% (0.3-3.2 keV).