It was the practice of the Prophet (peace and blessings be upon him):
"When he (peace and blessings be upon him) got up from sleep at night, he would clean his mouth with the tooth-stick (miswak)."
Hadith Referenceصحیح الجامع الصغیر / حرف الكاف / 4764
Hadith Gradingالألبانی:صحيح
Hadith Takhrij[حم ق د ن هـ] عن حذيفة. الروض ٢٨٣، صحيح أبي داود ٤٩، الإرواء ٧١.