And Peru followed suit on Friday, announcing an identical measure due to begin a week later.
The decision drew an immediate rebuke from authorities in Colombia with Colombia Migration Director Christian Kruger warning against the new passport rule.
Venezuelan migrants have been taking days-long bus rides across South America, often crossing Ecuador on their way south to Peru or Chile, because they can not afford flights on a minimum wage that adds up to a few US dollars a month.
In Ecuador, authorities estimated more than 4,000 Venezuelans entered each day in early August over the Rumichaca International Bridge.
Kruger said he was "worried about the consequences" for Rumichaca because around half of the Venezuelans heading south through Colombia are carrying only ID cards rather than passports.
"We are immensely anxious about the consequences this might present", he said.
According to the United Nations, 2.3 million Venezuelans have fled since 2014 as their country reels from hyperinflation and severe shortages of everything from food and medicine to ink and paper for passports.
Peruvian Interior Minister Mauro Medina said the passport requirement is needed to ensure an orderly migration.
"The exodus of Venezuelans from the country is one of Latin America's largest mass-population movements in history", William Spindler, the spokesman for the U.N. High Commissioner for Refugees, said earlier this month.
Peru's government said it is collaborating with Venezuela to locate the suspects and confirm whether or not they are in Peru.
'Also, some bad apples - who don't represent the majority, who are decent people - filter in and police should have the adequate tools to identify them'.
"Asking for a passport isn't going to stop migration because they're leaving their country not out of choice but out of necessity", added Kruger.
Many Venezuelans are aiming further afield to settle in Peru, Chile, Argentina or even Uruguay.
Kruger, the Colombian official, said the new passport rule is unlikely to stem the tide of migrants and called on Ecuador and other nations to work together on dealing with the crisis in crafting common-sense policies.
'This isn't a migration of people leaving their country just because they want to.