It is narrated from Sayyida Busrah bint Safwan (may Allah be pleased with her) that she heard the Prophet (peace and blessings be upon him) say: "When any one of you touches his private part, he should perform ablution." Imam Malik (may Allah have mercy on him) says that in his view, performing ablution after touching the private part is recommended (mustahabb); he does not consider it obligatory. Janab Ali bin Saeed Naswi says that he asked Imam Ahmad bin Hanbal (may Allah have mercy on him) about performing ablution after touching the private part, and he replied that he considers it recommended (mustahabb), not obligatory.
Hadith Referenceصحيح ابن خزيمه / جماع أبواب الأحداث الموجبة للوضوء / 33
Hadith Takhrij«اسناده صحيح ، سنن النسائي ، كتاب الطهارة ، باب الوضوء من مس الذكر ، رقم الحديث: 163 ، سنن ابي داود ، الطهارة باب الوضوء من مس الذكر: 181 ، سنن ابن ماجه: 479 ، موطا مالك: 87 ، سنن الدارمي: 726 ، أحمد 406/6 ، الحميد: 352»
Imam Abu Bakr, may Allah have mercy on him, says that I heard Muhammad bin Yahya saying, "According to us, due to the hadith of Sayyiduna Talq, may Allah be pleased with him, performing ablution after touching the private part is recommended, not obligatory." Imam Abu Bakr, may Allah have mercy on him, says that Imam Shafi’i, may Allah have mercy on him, instead of making analogy, used to declare ablution obligatory after touching the private part by following the hadith of Sayyida Busrah bint Safwan, may Allah be pleased with her. Imam Abu Bakr, may Allah have mercy on him, says that I also hold the same position as Imam Shafi’i, may Allah have mercy on him, because Hazrat Urwah heard this hadith from Sayyida Busrah, may Allah be pleased with her—contrary to the misconception of some scholars who say that this hadith is weak due to criticism of Marwan.
Hadith Referenceصحيح ابن خزيمه / جماع أبواب الأحداث الموجبة للوضوء / 34
Hadith Takhrij«اسناده صحيح ، سنن أبى داؤد ، كتاب الطهارة ، باب الرخصة فى ذلك ، رقم: 183 ، 182 ، الترمذي، رقم: 85 ، وابن ماجه، رقم: 483 ، أحمد: 22/4 ، 23»