The law requires permission from authorities before public protests can be held. Those who failed to get permission have often been treated harshly, especially under the former military regimes.
"We don't want to hit the streets again, but we must because the government used this law to detain and charge activists who didn't ask for permission from officials," said Ko Ko Gyi, a leader of the 88 Generation Students, the most prominent pro-democracy group in the country.
Up to 60 civil society groups are planning to demonstrate on Sunday against the law in the largest cities, Yangon and Mandalay.
Ko Ko Gyi said there had been 256 cases this year of activists detained and charged for protesting without permission.
He said the government should dismiss those cases, and comply with President Thein Sein's pledge to release all remaining political prisoners.