Opposition legislators oppose the bill which would allow Uganda's long-time leader to run again, and engaged in fist fights as well as shoving matches with ruling party members, local media reported.
According to reports, about two female lawmakers were rushed out of the hall to the hospital.
Should the bill be passed he would be able to serve a third term in office.
Tension in parliament has been heightened by a proposed motion that would prevent anyone over the age of 75 from running for president.
On Wednesday, in response to the violence in parliament, Museveni's government took its efforts one step further by announcing that it would ban live broadcasts of events "inciting the public", including parliamentary debate.
In 2005, a constitutional amendment was made removing the two-term limit for the presidency to allow the president to run for a third-term which he won in February past year, even though opposition unsuccessfully contested the outcome.
Putting Catalan Police Under Spanish Command Is a Bad Idea
That support has been waning in recent months as Spain's national and regional economies have begun thriving again. They would join the roughly 5,000 state police normally stationed in Catalonia and around 17,000 Mossos officers.
No station aired Wednesday's proceedings, but some posted clips of the brawls on their Twitter feeds.
Brawling erupted in the chamber, with some parliamentarians from the east African nation using chairs as weapons in the scuffle.
That makes Museveni, 73, in power since 1986 and increasingly accused of authoritarianism and a failure to curb corruption, unqualified to seek re-election at the next polls in 2021.
Protests by students, activists and the opposition have seen arrests around Uganda this week, with Uganda's leading opposition figure, Kizza Besigye, also being arrested.
Museveni, a USA ally on regional security, took power by force in 1986 and was re-elected previous year in a poll marred by allegations of fraud and voter intimidation.
The age-limit issue has been so contentious that last week Parliament had to be adjourned after MPs heckled each other, shouted at each other and whistled.