The Glasgow Kelvin MSP Sandra White is proposing legislation which would also make it illegal for vehicles to double park.
Her bill won unanimous support, but is unlikely to complete its passage through Parliament before the election.
The SNP government has pledged to legislate to tackle irresponsible parking if it returns to power after the May poll.
The Footway Parking and Double Parking (Scotland) Bill would make it illegal to park on pavements and dropped kerbs, and restrict double parking on roads.
It gained broad support from the public during consultation.
When Ms White's bill was originally introduced to the Scottish Parliament in May last year it was unclear whether Holyrood or Westminster has the power to legislate.
The powers have now been agreed as part of the package of further powers included in the Scotland Bill.
Ms White said she was "delighted" the bill had passed the first stage of the parliamentary process.
She added: "Reckless parking can make life extraordinarily difficult for those with mobility or sight issues as well as many other pedestrians. It's right that we make it clear that bad parking is unacceptable.
"After raising this issue for several years I am glad that we now have the power to act."
MSPs have voted in principle to make it an offence to park on pavements.