סימן פז סעיף כא

וְאִם כְּבָר הֻרְגְּלוּ וְהֵמָּה בְּנֵי תַּרְבּוּת שֶׁדַּרְכָּן לָבוֹא בָעֶרֶב לִמְקוֹמָם וְיָצְאוּ, וְהוּא חוֹשֵׁשׁ שֶׁלֹּא יִגְנְבוּ אוֹתָם, מֻתָּר לִדְחוֹתָן שֶׁיֵּלְכוּ לְמָקוֹם הַמִּשְׁתַּמֵּר. אֲבָל לֹא יִקַּח אוֹתָם בַּיָּדַיִם, שֶׁהֲרֵי הֵם מֻקְצִים.

If they are already trained and domesticated and usually return home in the evening but they went out, and you are worried lest they be stolen, you are permitted to drive them to a safe place,⁴³Since they are domesticated, even capturing them outright is only a derabanan prohibition; driving them is permitted. [v. Shulchan Aruch 316: 12; Mishnah Berurah, 316: 37; Chayei Adam] but you may not carry them by hand because they are muktzeh.⁴⁴If only capturing them by hand will keep them from escaping Mishnah Berurah (305: 70) seems to lean towards the ruling of Magein Avraham who prohibits handling muktzeh even where the loss of the animal may result.
Eliyahu Rabbah and Chazon Ish (52: 16) disagree and allow capturing them by hand to prevent the animal’s escape. See also Mishnah Berurah 308: 151.

תנא דבי אליהו כל השונה הלכות בכל יום מובטח לו שהוא בן העולם הבא שנאמר הליכות עולם לו אל תקרי הליכות אלא הלכות (נדה ע"ג.)