Praise be to Allah.
It is permissible for a fasting person to use miswaak and toothpaste whilst fasting, so long as he is careful not to swallow anything. In fact using the miswaak is Sunnah when fasting and otherwise.
Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said: As for the miswaak, it is permissible and there is no difference of opinion concerning that. But they differed as to whether it is makrooh after the sun has passed the meridian, and there are two well known views, both of which were narrated from Ahmad. But there is no shar’i evidence suggesting this to be makrooh which can be regarded as an exception from the general meaning of the texts about the miswaak. End quote from al-Fataawa al-Kubra (2/474).
The scholars of the Standing Committee for Issuing Fatwas were asked:
Can the fasting person wear perfume? Is it permissible for him to use the miswaak during the day? Can a woman put henna or oil on her hair?
They replied: he may put perfume on his clothes or on that which he wears on his head or body. But he should not put it in his nose.
He may use the miswaak during the day, because the Prophet (peace and blessings of Allaah be upon him) said: “Were it not that it would be too difficult for my ummah, I would have told them to use the miswaak before every prayer.” Saheeh – agreed upon. This includes Zuhr and ‘Asr prayer for the one who is fasting and for others, and we do not know of any saheeh evidence to suggest that this is not allowed.
A woman may put on henna or put oil on her hair, because that does not affect the fast. A man may also apply medicine and so on, even if he is fasting. End quote.
Fataawa al-Lajnah al-Daa’imah (10/328).
Shaykh Ibn Baaz (may Allaah have mercy on him) was asked: What is the ruling on using toothpaste when fasting?
Cleaning the teeth with toothpaste does not break the fast as is the case with the miswaak. But one should be careful to avoid letting any of it reach his throat, but if that happens accidentally then he does not have to make up the fast. End quote from Majmoo’ Fataawa al-Shaykh Ibn Baaz (15/260).
And Allaah knows best.