McLaren and Force India were among six teams that had accepted an invite to participate in a three day test in Bahrain between December 17th and 19th.
The test is being held at the behest of Pirelli in order to improve the safety and usability of the 2014 tyres.
The FIA revealed on Monday that all 11 teams were invited but only six took up the offer. Now McLaren and Force India, the teams which finished in fifth and sixth place in the 2013 constructors' championship, have pulled out.
'We are not testing in Bahrain next week', a McLaren spokesman told Sky Sports.
'Given the short notice of this test taking place and the time frames involved, the team will not be attending the test', Force India said.
2013 cars will be used in next week's test, which is currently set to include Red Bull, Mercedes, Ferrari and Toro Rosso.