We report the discovery of X-ray eclipses in the recently discovered accreting millisecond X-ray pulsar Swift J1749.4 - 2807 . This is the first detection of X-ray eclipses in a system of this type and should enable a precise neutron star mass measurement once the companion star is identified and studied . We present a combined pulse and eclipse timing solution that enables tight constraints on the orbital parameters and inclination and shows that the companion mass is in the range 0.6 - 0.8 M _ { \odot } for a likely range of neutron star masses , and that it is larger than a main sequence star of the same mass . We observed two individual eclipse egresses and a single ingress . Our timing model shows that the eclipse features are symmetric about the time of 90 ^ { \circ } longitude from the ascending node , as expected . Our eclipse timing solution gives an eclipse duration ( from the mid-points of ingress to egress ) of 2172 \pm 13 s. This represents 6.85 % of the 8.82 hr orbital period . This system also presents a potential measurement of “ Shapiro ” delay due to General Relativity ; through this technique alone , we set an upper limit to the companion mass of 2.2 M _ { \sun } .