The 31-year-old missed a 20-foot birdie putt at the 18th at the Oceanico Victoria Golf Club on Thursday to miss out by one stroke.
He posted seven birdies in his first 12 holes before eagling the 15th and 17th.
"Walking down 17, I told my caddie, 'it's 59 or nothing'," said Colsaerts.
"I managed to make an eagle and then hit a good drive on the 18th. It's too bad it just shaved the edge," he added of his putt.
A round of 60 has been achieved 19 times on the European Tour. American Peter Uihlein did so twice in 2013, as did Scotland's Scott Jamieson.
The latter sits three strokes adrift of world number 185 Colsaerts in Portugal, alongside Alexander Levy of France.
Play was suspended for the day because of rain, with 45 of the 125 players still to complete their first rounds.
Belgium's Nicolas Colsaerts came within millimetres of becoming the first man to shoot a sub-60 round in the 42-year history of the European Tour during the opening round of the Portugal Masters.