The 27-year-old forward, who joined the Toffees from Rangers in 2012, said: "I come from Ayrshire in the West of Scotland and spent a lot of my life in Glasgow - a city that, at times, has suffered from high unemployment.
"Liverpool has a similar history and I am aware that, through no fault of their own, there are many unemployed in Liverpool trying hard to find a job and may not be able to afford a ticket.
"I thought this might be a small gesture to help those in that situation to enjoy a day out at one of our league matches. Hopefully it can bring some joy to many people.
"I have asked the Jobcentreplus if they could give the tickets to different Jobcentres across the city each week and select people who are unemployed through no fault of their own, are trying hard to find employment and who would enjoy watching a Premier League football match."
Naismith is no stranger to charity work and helps homeless centres in Liverpool and Glasgow.
He also launched a project in Glasgow to help injured service personnel back to mainstream employment and is an ambassador for Dyslexia Scotland.
The Scotland international said: "Every day I feel very fortunate for the opportunities and lifestyle my job as a footballer has afforded my family and me and also to be in the position where I can help the community in some small way."