Museveni would have been barred from contesting in the next vote because he would be 76 years old.
Reuters reports Francis Gimara, president of Uganda Law Society (ULS) said that top lawyers had lodged a petition in court to nullify the law.
Critics accuse Museveni of plotting to cling on to power beyond 2021, and say he is the brains behind the removal of the age-limit.
Legislators allied to the ruling National Resistance Movement said they supported the removal of the cap to allow Museveni run again in 2021 as no one was fit to replace the long-serving leader.
Parliament debates on the law caused physical confrontations in parliament in September, with security authorities arresting and detaining some opposition MPs.