Can I block an IP address?

As you've never worked with packet filters, I'd strongly recommend reading the following first:

http://support.f5.com/kb/en-us/products/big-ip_ltm/manuals/product/tmos-implementations-11-3-0/24.htmlconceptid

http://support.f5.com/kb/en-us/products/big-ip_ltm/manuals/product/tmos-concepts-11-3-0/tmos_packet_filters.html1189342

As for the iRule, simply copy the above to a new iRule in the iRules section of the management GUI, and change the xx.xx.xx.xx/xx do a specific IP address (ex. 123.45.678.90) or a specific subnet (ex. 123.45.67.0/24), then add that iRule to the virtual server configuration. You could even throw in some logging to see what IP address is getting blocked (and when).

when CLIENT_ACCEPTED {
    if { [IP::addr [IP::client_addr] equals xx.xx.xx.xx/xx] } {
        log local0. "Blocking [IP::client_addr]"
        reject
    }
}