The note, which has gone viral on Imgur, praised the dad for being a good role model for his six-year-old daughter.
The anonymous message read: "Hi there, Sorry to spy but my husband and I saw you out with your little date and were so impressed with what a great dad you are.
"From two adults who grew up without dads, it's so important to have a male role model at a young age.
"Keep up the good work dad! Dinner is on us!"
A picture of the note was posted on the social media site imgur, with the headline 'I wish I could thank them'.
Beneath it, the poster wrote: "As a single dad, I took my six-year-old daughter out to Valentine's dinner tonight when this happened.
Since then, hundreds of people have posted positive messages of support on the site.
One wrote: "So important. So damn important. Her future expectations are set on these memories. You are the best."
Another said: "The satisfaction you'll get when she remembers dinners like this."
And one single dad added: "As a single dad of a little girl... HOW COME THIS NEVER HAPPENS TO ME?!?! (Oh, right, mine's 12 now, and not six.)."
Another user wrote: "Thats awesome! Good on them and good on you :) My dad is my hero, she will always remember these."
And this reader added: "This made me tear reading it, because my son's father barely comes to see him anymore. It makes me happy to know men like you exist."