A business certification recognized by the Prime Minister and Minister of Economy, Trade and Industry.
「内閣総理大臣及び経済産業大臣事業認定資格」は英語で「A business certification recognized by the Prime Minister and Minister of Economy, Trade and Industry.」と言います。履歴書を英語で書く時はおそらく項目の下に書くので、以下のように書いたら問題ないと思います。かっこつけて項目の隣に入れても大丈夫だと思います。
例1)(資格)
-Recognized by the Prime Minister and Minister of Economy, Trade and Industry.
例2)~~~ Certification (Recognized by the Prime Minister and Minister of Economy, Trade and Industry.)