How can I replace parameter by subdirectory

Currently I have my search page hosted like below

mywebsite.com/search.html?query=cat

So I am extracting query from url parameter as you can see the query is 'cat' for now.
For some seo reasons this is not a good practice so I want to replace above format to following format:

mywebsite.com/search/cat

Is there any way to achieve such result without actually changing the current files? Right now I am hosting the website with nginx in ubuntu server. Any suggestion is hugely appreciated.

Thanks in advance