The Scots are already reeling from the losses of pivotal figures including Finn Russell, Stuart Hogg, WP Nel, Huw Jones and Ryan Wilson. Strauss played in Scotland's opening two games of this year's competition against Italy and Ireland and was expected to be involved again this weekend.
The 32-year-old, who qualified to play for Scotland through residency, is a South African citizen and would require a passport with a visa to travel to France.
"We are working with the relevant authorities to secure Josh's safe passage to Paris," a Scottish Rugby spokesperson said after the passport loss was reported in the Sun newspaper.
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The Sun said Strauss was unable to get a replacement document in time for the weekend's match.
Secretary of State for Scotland David Mundell is attempting to help Strauss secure the right to travel to France, it added.
(Reporting by Mark Gleeson; Editing by Alexander Smith)
