The closure of 11 pillar boxes in the Yorkhill area has forced customers to use neighbouring post offices until locks are changed.
Local Stewart Gibson, who went to post a crossword competition entry only to discover metal plates had been fitted to three of the boxes, said he was angry at the inconvenience.
The 59-year-old administrator was forced to go to a post office where he discovered four other people had turned up with letters too.
He said: "I asked why the pillar boxes were blocked up but got no response."
Royal Mail chiefs admitted 11 boxes had to be sealed after a bunch of keys went missing over the Christmas period.
A spokeswoman said: "I am afraid that we have had to temporarily seal a small number of post boxes in the G3 postcode area due to keys going missing.
"We are waiting for new locks to come from our supplier and as soon as they arrive we will fit them and reopen the boxes.
"We apologise to customers for any inconvenience caused while the boxes are out of action."
She added: "There is no master key.
"Every individual pillar box has an individual key."
Mr Gibson said: "I can't understand why there is no master key. Most businesses have a master key because keys do go missing.
"However, what really annoys me is the way Royal Mail has not kept customers fully informed.
"They could have put notices up at local post offices to alert people to the situation but there was nothing."
Postal bosses revealed the keys had gone missing after being contacted by the Evening Times.
They' also admitted having keys to just two other pillar boxes in the Yorkhill area.
The spokeswoman added: "In the meantime customers can use other boxes in the area at North Claremont Street and Park Circus or the Post Office branches at Sandyford, 1195 Argyle Street, and Charing Cross and 533 Sauchiehall Street."
It is not known when new locks will be fitted to the affected boxes but the work is expected to be carried out over this month.
An internal inquiry is also thought to have been conducted into the missing keys.