Carwyn Jones said it would "diminish not just the United States in the eyes of the world, but the west as a whole".
Mr Trump's executive order also halted the entire US refugee programme.
Mr Jones said the impact on "law-abiding citizens" is "beyond any rational defence".
"Those of us who believe in the solemn duty of helping and protecting refugees must now work harder to show that help is still available and that we still care," he added.
Mr Trump has said it is part of new measures to "keep radical Islamic terrorists out of the US".
Mr Jones also criticised Prime Minister Theresa May's response to Mr Trump's executive order.
Mrs May initially said the USA's immigration policies were a matter for them, not her, before Downing Street said she "does not agree" with the entry ban.
"If the special relationship means anything, it must mean honestly calling one another to account. Silence and evasion are not the hallmarks of leadership," Mr Jones added.
He said he would be raising the matter with Mrs May when they meet on Monday for the Joint Ministerial Committee.
Plaid Cymru leader Leanne Wood said the policy risked "fuelling grievances of those already marginalised in our communities, giving rise to further alienation and undermining security".
She added: "Trump's actions have rightly been met with anger around the world and should be condemned without reservation by us all."
The first minister has criticised President Donald Trump's decision to institute a 90-day travel ban for nationals from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.