The bridge, which leads to the Islamic State group held old city centre from the south, is the second to be seized by anti-IS forces since February 19.
"We control the western end of the bridge," said a senior media officer with Rapid Response, the interior ministry's elite unit that is heading the advance through districts along the Tigris river.
While all of Mosul's five bridges have been destroyed, their capture and repair could hasten the defeat of IS militants who have held the northern Iraqi city as their 'capital' since 2014.
After over three months of fighting, Iraqi forces have managed to capture Mosul's eastern side.
On Sunday, it was also reported that a cousin of IS leader Abu Bakr al-Baghdadi had been captured by security forces.
Video emerged on social media showing Iraqi soldiers parading a bearded man through the streets as some took selfies with the reportedly high-ranking IS figure.
The capture of an individual linked closely to the IS leader would prove a major blow to the extremist group, who lost seven commanders in US-led airstrikes on Friday.
Another senior commander was also arrested on Saturday.
Iraqi forces are currently advancing toward Mosul's old city centre form the south and the southwest.
The battle for the city, which has raged on for over 100 days, has displaced over 200,000 people as fierce street-to-street fighting ensue between pro-government forces and IS militants.
Aid agencies estimating that around 750,000 people remain in the city, which is the IS group's last major Iraqi stronghold.