Only those who have registered for a special border card or can produce a passport will be able to cross.
They fear it will become more difficult for them to enter Colombia once the measures are fully implemented.
Thousands of Venezuelans cross into Colombia daily to look for temporary work or to buy essential goods.
Most of them return home, but the Colombian government expects many more to stay permanently as Venezuela’s economic crisis worsens.
Venezuela has suffered for years from high inflation and the chronic shortage of food and medicines.
Brazil has also expressed concerns, with thousands of Venezuelans are living in precarious accommodation in the border state of Roraima.
Venezuelans will go to the polls on 22 April to vote for president.
Nicolás Maduro, who has been in office since 2013, is running for a second six-year term.
He says the crisis has been caused by economic sabotage sponsored by the US.
The Venezuelan opposition is weakened and is yet to choose a candidate.
It blames the policies of the Socialist Party, in power since 1999, for the collapse of the oil-rich country’s economy. (Courtesy BBC)