The US biotech company is alleging that mRNA technology it developed before the pandemic was copied.
The lawsuit, which is seeking unspecified financial damages, was filed in the US and Germany.
Pfizer said it was "surprised" by the action and would "vigorously defend" itself against the allegations.
In a statement, Moderna said Pfizer/BioNTech copied two key elements of its intellectual property.
One involves a "chemical modification" which Moderna says its scientists were the first to demonstrate in human trials in 2015, and means the vaccine "avoids provoking an undesirable immune response".
The second alleged infringement is related to the way both vaccines target the distinctive spike protein on the outside of the virus.
"We are filing these lawsuits to protect the innovative mRNA technology platform that we pioneered, invested billions of dollars in creating, and patented during the decade preceding the Covid-19 pandemic," Moderna chief executive Stephane Bancel said.
Moderna, which was only formed as a company in 2010, was an early developer of the mRNA technology used commercially for the first time in Covid vaccines.
The jabs use a molecule of genetic code called messenger RNA to generate an immune response.
That trains the body to fight off the real virus when it comes into contact with it.
Early in the pandemic, Moderna said it would not enforce its patents to help other drug companies develop their own jabs, particularly for low- and middle-income countries.
In March 2022 it said rivals such as Pfizer and BioNTech would have to respect its intellectual property rights in some higher-income countries, though it would not claim damages for activity before that date.
Patent disputes often take place when new technology is developed and both Pfizer/BioNTech and Moderna are already facing other lawsuits relating to their respective mRNA platforms.
Moderna itself is in an ongoing dispute with the US National Institutes of Health over the credit for key patents relating to mRNA technology.
In July, German biotech company CureVac filed a lawsuit against BioNTech claiming it violated patents linked to the engineering of certain mRNA molecules and seeking "fair compensation".
In a statement Pfizer said it had not yet fully reviewed Moderna's complaint but was "surprised" given that its vaccine was based on its own proprietary mRNA technology.
A spokesperson for the company said: "We remain confident in our intellectual property supporting the Pfizer/BioNTech vaccine and will vigorously defend against the allegations of the lawsuit."
-- Courtesy of BBC News