To make itself a "welcoming and safe place for everyone," Instagram will let users disable commenting on any of their posts. If you're concerned about the sort of statements people may post in response to your pictures, this feature may be helpful, especially since Instagram isn't as focused on interaction as Facebook or Twitter.
Instagram has rolled out the ability to a few accounts and others will receive it "in the coming weeks."
These updates still mark the beginning. We will continue to work to maintain Instagram as a welcoming and safe place for everyone. - Kevin Systrom, CEO, Instagram
Another update being applied to the network lets users like comments by tapping a heart next to them. This is similar to liking comments on Facebook, Instagram's parent company.