Barcelona's teenage winger Yamal "reported discomfort in his right knee" after their 2-1 win at Atletico Madrid in La Liga on Sunday.
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Real Sociedad forward Oyarzabal "is in the final phase of a bout of flu", explained the federation.
"Both players will join the training camp in the coming days so they can be available to face England at the Metropolitano Stadium (on Sunday)," added the RFEF.
World champions Spain, who have already qualified for the Nations League quarter-finals, visit the Czechs on Thursday before hosting Thomas Tuchel's England in Madrid.