The eight soldiers are part of a mission to provide the Palestinian Authority Security Forces with training advice and support, and have been overseas for a year.
The strike at the Israel Foreign Ministry has meant replacements, due to arrive this month, are not able to get the visas processed.
A spokeswoman for National Defence, Elana Aptowitzer, says Canadian officials are working on the situation and soldiers on the ground have been told "their deployment may be extended by a few weeks."
The Defence Department remains optimistic there will be "no significant delays" even though job action at the Israeli foreign ministry has been going on since March, with no promise of a resolution, and a mounting list of commercial tours are being put in jeopardy or cancelled.
Among other things, the employees won't issue diplomatic passports to Israeli ministers, and have shut down communications between Israeli missions abroad and the Foreign Ministry in Jerusalem, as well as refused to arrange official visits of Israeli cabinet ministers to other countries.