Alison Thewliss, the SNP MP for Glasgow Central, has written to all 42 league clubs north of the border to press her case that it “need not be a taboo issue”.
The Motherwell supporter said she was inspired to do so by championship side Ayr United, which recently declared its Somerset Park stadium a breastfeeding-friendly ground.
The lifelong football fan is now encouraging other clubs to follow suit.
She said the move has already received a “fantastic” reaction, with more than half of the clubs saying they are taking up the initiative.
Breastfeeding in public places has been a legally protected right in Scotland since 2005.
Ms Thewliss said places that declare themselves breastfeeding-friendly give additional reassurance to mothers.
She said: “Football crowds have changed a lot over the years and stadiums are becoming a much more family friendly environment. The vast majority of clubs understand the need to build future generations of fans.”
The MP told how she took her son to Motherwell’s Europa League game against Aalesund when he was a month old.
“I was a bit nervous about doing so, but was very much supported by my family and neighbouring fans,” she said.
“I’ve had a positive experience at Scotland games too, and I would encourage all clubs to play their part.”
Ms Thewliss added: “By making a positive declaration that stadiums are breastfeeding-friendly, this will go some way to letting people know that breastfeeding is normal and need not be a taboo issue.
“With the exception of one or two clubs, the initial response from the majority of Scottish football clubs has been absolutely fantastic and it’s encouraging that so many folk are uniting to make Scottish football a breastfeeding-friendly environment”.