The postponements come as the coronavirus pandemic begins to impact architecture and design events beyond the summer and into next year.
The five-day Biennale Interieur will now be held at the Kortrijk Xpo fairground from 21 to 25 October 2021.
Tallinn Architecture Biennale has yet to announce dates for its revised event, which will now be held in 2022 instead of 2021.
The impact of the Coronavirus is immense," says Biennale Interieur CEO Jo Libeer. "Uncertainty reigns and investments big and small are being postponed."
"As an organization, we have to take up responsibility both towards our exhibitors as towards our visitors," he added.
"Since we want to guarantee our known level of quality, we have decided to postpone the 27th edition of the Biennale Interieur by one year".
The annual Belgian designer of the year award will still take place this autumn as scheduled, organisers announced.
The fair has been held in the Belgian city of Kortrijk every two years since 1968 and celebrated its 50th anniversary in 2018. It attracts 50,000 visitors.
The Estonian Centre for Architecture, which organises the Tallinn Architecture Biennale (TAB), announced that the event will now take place in 2022.
"The peculiar times we live in has given us an extra year for the organisers and the head curator to prepare for the upcoming edition of TAB," said Estonian Centre for Architecture director Raul Järg.
"This ensures enough time for a high-quality theme and a comprehensive programme. We hope that the teams who are participating in the curatorial competition understand the decision and are ready to contribute also in 2022."
TAB was first held in the Estonian capital in 2011. The competition to find a head curator for the next event will go ahead as planned. The deadline for submissions is 29 May 2020.
Virus impacts events beyond summer 2020
Biennale Interieur and TAB's postponements follow news that September's London Design Biennale has been moved to 2021 following similar announcements from key summer and autumn events including the Venice Architecture Biennale, Dubai Expo 2020 and the Tokyo 2020 Olympics.
For more details of events impacted by Covid-19, check the dedicated page on Dezeen Events Guide.
Main image by Jeroen Verrecht.