You can restrict by hosted zone, but not by sub-domain. Your Route53 hosted zones should be split up by subdomain if you'd like to restrict to specific subdomains. You can create a hosted zone for a subdomain:
For example if you wanted a subdomain named test you can do as the answer here summarizes well:
Create a hosted zone for test.example.com.
Note the 4 name servers that Route 53 assigns to it the new hosted
  zone.
Back in the master zone, create a new resource record, with hostname
  "test" using record type NS, and enter the 4 name servers that Route
  53 assigned, in the box below.
The above delegates control of that subdomain to this new hosted zone, which has a unique zone id we can use in an IAM policy
You can then build an IAM policy that restricts actions to this zone:
{
   "Statement":[
      {
         "Action":[
            "route53:*"
         ],
         "Effect":"Allow",
         "Resource":[
            "arn:aws:route53:::hostedzone/<The new zone ID>"
         ]
      },
      {
         "Action":[
            "route53:ListHostedZones"
         ],
         "Effect":"Allow",
         "Resource":[
            "*"
         ]
      }
   ]
}
From here you can tweak this policy to fit the actions you'd like the user to be able to take in this zone.