His office said he wanted to apologise to the child and his family "for the hurt his words may have caused".
BBC reports the video also shows the Dalai Lama kissing the child on his lips.
"His Holiness often teases people he meets in an innocent and playful way, even in public and before cameras. He regrets the incident," his office said.
The footage has sparked widespread criticism, with many social media users saying it was inappropriate and disturbing.