It was one of 20 left at various locations by Ren Benson, from York, who said she just wanted to give other mothers support.
"I am a first-time mum, my little boy is 10 months now, and parenting is really hard," she said.
Emma Lowe, who found the supermarket letter, said it was a "lovely gesture" and very welcome.
Read more about this and other stories from across Yorkshire
On parenting, Miss Benson said: "It is really challenging and there are times when you do feel like you are just on your own and a little bit falling apart."
The first letter was left after she had dropped her shopping in the supermarket and felt she was at the "end of her tether".
"I thought 'this is the time when I need some love - there must be another mother who is going to feel this way'," she said.
Miss Benson said she was inspired by other mothers' random acts of kindness for each other through the online community - The Motherload.
"Such a small gesture and it can make the world of difference at times."
Mrs Lowe found the letter as she changed her daughter and said it had made her day.
"I ignored it at first, but on the envelope it said 'yeah you'.
"I opened it and thought what a lovely, lovely gesture that someone has taken the time to handwrite the note to say 'you know you've got this'.
"As a first-time mum it is really challenging at times, but I thought that is so lovely that someone has done that and left it for someone to find."

Captcha checks typically ask people to complete a puzzle that a computer would struggle to complete correctly.
They are designed to stop automated bots accessing and using websites.
Google's new system tracks how a person interacts with a website to prove they are real, so the puzzles are no longer necessary for most people.
Captcha checks are often deployed by concert ticket websites to stop people setting up automated bots to buy all the best tickets. They also appear when somebody is trying to log in to a website with the wrong password, to spot automated attempts.
The puzzles present challenges that people find simple but computers can find more difficult, such as:
The puzzles also benefit companies such as Google by helping train artificial intelligence algorithms. For example, if Google's AI can not recognise a house number in a photograph taken by a Streetview car, it may add the photo to its Captcha system to get human input.
However, genuine users can find the interruption by puzzles a nuisance.
Google's reCaptcha system has already simplified the process by asking users to tick a check box on the website they are using. The box monitors how each person has interacted with it, to separate natural human clicks from bots.
For example, an automated script might take just a second to fill in a form on a website, and may not move the mouse at all during the process.
Google's latest development removes the check box as well, and instead analyses how people have interacted with other elements on a website such as the "submit form" button.
However, in some cases "suspicious" activity will still trigger a puzzle.

RTÃ‰ reports that a number of flights have been cancelled at Cork airport and weather warnings are in place.
A number of power outages have also been reported with about 25,000 customers affected.
Aer Lingus regional flights to and from Edinburgh, Birmingham, Manchester and Bristol have been cancelled.
This is also the case with some City Jet flights to and from London City Airport.
The airport is advising intending passengers to check with their airlines.
There have also been some flight diversions from Dublin Airport to Belfast due to the weather.
A handwritten letter of encouragement for new mothers was left in a supermarket baby-changing area.
[NEXT_CONCEPT]
Website security checks that challenge people to prove they are human are likely to "disappear" in favour of a new system developed by Google.
[NEXT_CONCEPT]
Thousands of people are without power in the Republic of Ireland as the effects of Storm Barney take hold.