The reward comes after the animal was shot in an estuary in the Catlins then left to die a slow, painful death.
Posting on social media, the Sea Lion Trust said they needed to send a message that such acts were not acceptable.
"Not only has an endemic species been deliberately killed with a shotgun, but it has been done in such a way that it will have suffered a slow and painful death.
"It is important that we learn to share our spaces with other species and remember the beaches, the ocean, the fish, are not ours, but belong to all."
Sea lions were "charismatic and curious" animals, which sometimes approached people - making them vulnerable to harm, the trust said.
"The loss of this young female sea lion is another blow to a small, establishing population that has already experienced low pup survival over the last couple of years."
The same pup attracted attention earlier this year when she was born about 60km up the Clutha River near Tuapeka.
Anyone with information should contact the New Zealand Sea Lion Trust at info@sealiontrust.org.nz or your local police, it said.
"All information will be passed on to the appropriate authorities and anonymity will be respected.
"This reward does not offer immunity from prosecution, and will be paid out after a conviction."
