Elite troops captured al-Muthana following night-time fighting, an army spokesman said, putting them in a position to take higher ground nearby.
It comes days after Iraqi forces began the second phase of a push to conquer the last major IS stronghold in Iraq.
About two-thirds of east Mosul has been retaken since October, officials say.
The army said its troops had raised the national flag after capturing al-Muthana.
Counter-Terrorism Service (CTS) spokesman Sabah al-Numan told Reuters news agency soldiers had attacked by night for the first time, crossing a tributary of the River Tigris.
"We used special equipment and had the element of surprise - the enemy did not expect us to mount a night offensive because all previous offensives were during the day," he said.
On Wednesday the commander of the US-led coalition against IS said Iraqi forces were gaining momentum in Mosul, in northern Iraq, after the campaign had almost ground to a halt by December in the face of fierce resistance by IS.
Lieutenant General Steve Townsend said this was partly due to improved co-ordination between Iraqi commanders from various pro-government forces involved in the operation.
It also coincides with a sharp increase in the number of military advisers from the US and other coalition countries helping with the battle.
The offensive to recapture the city of Mosul was launched on 17 October, more than two years after jihadists overran the city before seizing control of much of northern and western Iraq.
Iraqi security forces, Kurdish Peshmerga fighters, Sunni Arab tribesmen and Shia militiamen, assisted by US-led coalition warplanes and military advisers, have been involved in the fight.
More than 100,000 people have fled their homes in and around Mosul and UN officials are warning that this figure is likely to rise as pro-government forces press further into the city.
Iraqi forces have made fresh progress in the battle against so-called Islamic State (IS) in Mosul, reportedly taking a key district in the city's east.