Short answer
No. The small cap many Muslim men wear is a kufi, taqiyah or topi, a Muslim tradition and not a yarmulke. A Muslim should not wear a kippah, because it is a Jewish religious sign, and wearing the religious signs of another faith is forbidden imitation.
Wearing the distinctive religious dress or symbol of another faith is haram. Covering the head with a cap or turban is a commendable sunnah of habit for Muslim men, not an obligation.
The four schools agree on this.
Explanation
From a distance a white crocheted kufi and a kippah can look alike, but they come from different traditions. Muslim men have covered their heads with caps and turbans since the time of the Prophet ﷺ, who usually wore one or the other. For Muslims it is a sunnah of habit and a sign of dignity, not a duty; see do Muslim men have to cover their heads.
The kippah, by contrast, is worn by Jewish men as a sign of their faith. The Prophet ﷺ said whoever imitates a people is one of them, and he told Muslims to be distinct from the Jews and Christians of his time in matters such as dyeing grey hair. The Hanafi scholars apply the strictest ruling to religious symbols: wearing a cross, a priest's dress or a kippah is not allowed.
- Kufi, topi, taqiyah, Turkish or Malay cap, turban: all Muslim head coverings and all fine.
- A kippah, even as a courtesy at a Jewish event: decline politely; if a head covering is expected, your own Muslim cap does the same job. Good relations do not require wearing another faith's symbols.
- Respect: Muslims are taught to treat people of other faiths with fairness and good manners.
For turbans, see is wearing a turban sunnah, and for the rule on imitation, dressing like non-Muslims.
The evidence
Sunan Abi Dawud 4031
Graded hasan sahih... من تشبه بقوم فهو منهم ...
"Whoever imitates a people is one of them."
The basis of the rule against copying what is distinctive of another religion.
Sahih al-Bukhari 3462
Sahih... إن اليهود والنصارى لا يصبغون فخالفوهم ...
"The Jews and Christians do not dye their hair, so be different from them."
Muslims are told to keep a distinct identity.
Where the ruling is recorded
- Radd al-Muhtar (Ibn Abidin), Kitab al-Salah, chapter on what is disliked in prayer, discussion of imitation. Imitating another religion in its distinctive signs is forbidden.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.