FEDEX outlet at ZRH Airport ( owned and operated by someone else, not FEDEX ) is staffed and only accepts small packages and documents. They refused a 5kg package, so I guess packages must be really small and light to be accepted at that drop off outlet.
All accepted documents and packages are then sent to Fedex at Glattbrugg once daily. The outlet even encourages you to go there and drop it off at Glattbrugg.
Swissport Ticket Center
BZPB / Check-in 2
8058 Zurich-Flughafen
Phone: 0848 1 33339
Fax: +41 43 812 98 86
Maximum weight allowed: 5kg
08:00-19:00 Mon-Fri
FEDEX
Feldeggstrasse 3
8152 Glattbrugg
Phone: 0848 1 33339
Fax: +41 (44) 811 91 01 08:00-18:30 Mon-Fri
Source:
http://fedex.com/ch/dropoff/dropoff.html