This is definitely something you want to nip in the bud!
Here are a few things you might try:
Talk to your child about the fact that God gave us hands to love, help, pray, etc.
Sing “Be Careful What You Do Little Hands.”
Share 2 Timothy 2:24 – “Be gentle to all”. Make up a song using the verse and naming who or what we should be gentle with: be gentle to your friends, your pets, your books, etc.
Demonstrate a gentle touch.
Find pictures of children hugging or touching an animal gently.
Pray with your child, asking God to help him be gentle to all.
You might try putting him in his crib to isolate him. Tell him he can come out when he learns to control his hands and be gentle.
Read Under Loving Command (Children Fun or Frenzie) for some really helpful discipline pointers.
Don’t give up! Be consistent and pray. You will see the fruit of your labor – the fruit of gentleness which is one of the 9 fruit of the spirit!