Dan, 33, and his wife Abby announced the sad news on Wednesday via Instagram.
The musician continued, "We knew when we adopted her at age 16 with terminal cancer that our time together would be limited, but it's still never easy saying goodbye to a loved one."
"She was safe in our arms as she left us peacefully, and for that we are grateful," Dan added.
The singer went on to thank his "superhero wife" for "dedicating every waking minute to this sweet girl: from hand-feeding each meal, to giving her all the happy days in the sun."
"Missy, we love you and you'll always hold a special place in our hearts. may all your days be sunny, and your little tail never stop wagging. And to all of you who have so kindly followed her story, thank you. someone once said, 'dogs lives are too short. their only fault, really.' truer words have never been spoken," Dan concluded the tribute.
Abby, 32, also wrote a sweet farewell message about their fifth rescue.
The dog lover said, "We are still processing and honestly have taken this a lot harder than I think either of us could have imagined. We knew ultimately this would be the outcome, sooner rather than later, given her age and overall health but the rapidness of her decline has left us both a little rattled."
The couple adopted the rescue in late February when she was already in declining health, but Abby expressed that she has "no regrets in our choice to adopt a hospice dog and I will cherish our time together, it was so much longer than we ever could have thought in the beginning."
She later added, "I'm so grateful to have been Missy's retirement home."
"The hardest part right now is the day to day, caring for her was a major part of my life the last few months and I miss it a lot and mostly her sweet, tiny, crooked smile. Thank you to everyone who loved and rooted for her along with us. I know she touched so many," Abby said. "We miss you so much, little one."
Dan first introduced Missy in February, revealing that she was "16 years old. emaciated. no teeth. etc. all alone and terrified at the shelter."
The "Speechless" singer added, "We weren't going to let her live the rest of her life like that."
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"We're glad this tiny pup is safe now and finally getting to feel love (possibly for the first time). she's making great strides, and we even saw some tail wagging this afternoon (😭)," he wrote at the time.
Dan and Abby adopted Missy from Wags & Walks Rescue Nashville.
The elderly dog was their fifth rescue. Their other dogs include Joy, Chief, Ghost, and Mac.