tlmgr uses one of two download methods: The preferred ones is
LWP (Perl module), if that fails, it falls back to
LWP supports proxying, thus it should work (I cannot confirm it as I don't have a proxy running).
What you need is documented in the LWP manpage, but I copy it here:
These environment variables can be set to enable communication
through a proxy server. See the description of the "env_proxy"
method in LWP::UserAgent.
We already set enable proxies in the
LWP instance, so it should be enough to set the
http_proxy variable (and export it).
Incidentally (not really),
wget evaluates the same variables, so in case the
LWP method fails, also
wget should use the proxy.