Slot said the Englishman had struggled to adapt to the Dutch side's more rigorous sessions.
Reports in Holland claimed Nelson had joined Feyenoord in a poor state of fitness, having signed on loan on deadline day.
He was expected to be in the squad to play Maccabi Haifa in the Europa Conference League on Tuesday, but Slot has ruled him out.
"Nelson had participated in almost all training sessions at Arsenal, but he experiences the training here as a bit more intense," Slot explained at his pre-match press conference.
"He suffered an overuse injury and so he is not here. Whether he will make it to PSV [at the weekend] remains to be seen. At least not as a starting player."
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