Like it's been mentioned, this wouldn't be a DBI feature, but a database (DBD) feature, since some databases (like DBD::SQLite) don't even use sockets.

If you want a generic solution or a solution for databases don't have DBI or native support for encryption, you can create a secure (ssh) tunnel and give DBI the address of the tunnel instead of the address of the database server.

(Oops, Beaten to the punch!)