"Yesterday, we lost a precious young man in a tragic accident," a statement from St Luke's, obtained by the media outlet, said.
"Both St Luke's School and Brunswick School are in shock as we work to support our students and families. St Luke's singular focus at this moment is to care for our devastated community."
Brunswick posted a poem by A E Housman to its Instagram account titled To An Athlete Dying Young.
Camp Awosting, where Teddy had been a keen camper, shared a tribute to the teen on Facebook.
"Whenever Teddy entered a room, smiles followed, happiness ensued, our angel, our loss … We will miss you and we love you," the post read, alongside pictures of Teddy.
The local hockey community has shown its support on social media.
"We woke up this morning with the heaviest hearts after hearing of the tragic loss of one of New Canaan's own," New Canaan Hockey wrote on Twitter.
"Teddy was a wonderful young man, always smiling, a terrific teammate. No words are adequate for the grief we are all feeling. Our prayers are with Teddy and his family."
Others shared pictures of hockey sticks by their front door in honour of the boy.
Students in 10th grade in the US are usually 15 or 16 years old.