Ms Forbes and her husband, Ali MacLennan, said they were “delighted to welcome” their daughter into the world.
The couple said that both mother and baby are now back home and doing well.
The Skye, Lochaber and Badenoch MSP said: “We are delighted to welcome little Naomi into the world. It is a wonderful blessing to have a happy, healthy baby in our arms.
“Our family would like to record our most sincere thanks to the midwifery and nursing team at Raigmore for all their help.
“They were with us every step of the way, regularly going beyond the call of duty in their care and compassion for both me and Naomi.
“Pregnancy, labour and the early days with a newborn aren’t easy, as every new parent knows.
“Every mother’s experience is unique. Access to such excellent NHS healthcare in the community and at the hospital has made all the difference to us.”
Ms Forbes said it has been “hard” not to reflect on the hardships being faced by expectant and new mothers around the world, “particularly those escaping war zones like Ukraine or facing horrendous distress in Afghanistan”.
She said: “My prayer is that little girls around the world, like Naomi, grow up in a world of greater peace and security.”
Fellow parliamentarians took to social media to congratulate the couple on their new arrival.
First Minister Nicola Sturgeon tweeted: “Lovely news. Welcome to the world, Naomi – and many congratulations, Kate and Ali.”
Scottish Conservative MSP Murdo Fraser wrote: “Congratulations to you both. Great news!”
And Scottish Liberal Democrat leader Alex Cole-Hamilton said: “This is wonderful news, Kate. Huge congratulations!”
Ms Forbes and Mr MacLennan married last summer in the Highlands, following her re-election for a second term as MSP for Skye, Lochaber and Badenoch.
She will now take a period of maternity leave, and will return to work at some point in 2023.
John Swinney is covering the role of finance secretary for the duration of her absence, in addition to his duties as Deputy First Minister and Cabinet secretary for Covid recovery.