The Albertan, who has a longstanding interest in fossils, was digging a basement for a new home in Calgary's north-west.
Mr Nernberg is, according to reports, a donor to Alberta's Big Valley Creation Science Museum.
However, he realised these fossils should be seen by a palaeontologist.
"When the five fish fossils presented themselves to me in the excavator bucket, the first thing I said was you're coming home with me, the second thing was I better call a palaeontologist," Mr Nernberg said, according to a statement from the University of Calgary.
The specimens were in sandstone from the Paskapoo Formation, a Palaeocene age sedimentary rock which underlies parts of southern Alberta.
About 60 million years old, these rocks preserve evidence of life from the time following the mass extinction event at the end of the Cretaceous period, which wiped out three-quarters of all species on earth, including the dinosaurs.
"Because complete fossils are relatively rare from this time period in Alberta, any such discoveries are significant as they shed light on the nature and diversity of animals that lived not long after the extinction of the dinosaurs," said University of Calgary palaeontologist Darla Zelenitsky.
According to the university, all fossils in Alberta are the property of the province, and do not belong to the landowners or the finders.
While the university makes no mention of finder Edgar Nernberg's creationist links, Canadian newspapers have made much of them.
The Calgary Sun asked the "good-natured" Mr Nernberg if his find had affected his view that the earth was created 6,000 years ago.
"No, it hasn't changed my mind. We all have the same evidence, and it's just a matter of how you interpret it," he told the paper.
"There's no dates stamped on these things."
But Dr Zelenitsky - while she might disagree about fossil dating - praised Mr Nernberg for his awareness of what the fossils were.
"Most people would have overlooked these - when these were uncovered, Edgar right away recognised them," she told the paper.
"An ordinary person might have just seen blobs in the rock."
The fossils will now go to Alberta's Royal Tyrrell Museum, where they will be cleaned and studied, and may end up on display.
When Calgary digger driver Edgar Nernberg came across five fish fossils in his digger bucket, he knew right away his find was "extraordinary".