Are Tampons Haram?
Question

Does it state anywhere in the Quran or any Hadith that it is not permissible for Muslim sisters to use tampons?
Praise be to Allah.Islam: A religion of cleanliness
The Muslim is always commanded to avoid najasah (impure things), because Allah says (interpretation of the meaning): 
“And purify your garments!” [al-Muddaththir 74:4]
Are tampons haram?
Menstrual blood is najis (impure), and if it gets on a woman's clothes, she has to wash them. 
With regard to these tampons, we should refer to what women customarily use. At the time of the Prophet (peace and blessings of Allah be upon him), the women used to wear special clothes at the time of menstruation. 
Umm Salamah (may Allah be pleased with her) said: “My period came when I was with the Prophet (peace and blessings of Allaah be upon him), so I slipped away from him and put on the clothes I used to wear when I was menstruating…” (Narrated by al-Bukhari, al-Hayd, 311). 
And the general guideline is that things are permitted unless there is evidence to indicate that this is not allowed. 
So, it is not correct to say that using tampons is haram in Islam. In fact, there are reports which indicate that it is permitted to use cotton to stop the flow of blood. 
Hamnah bint Jahsh menstruated at the time of the Messenger of Allah (peace and blessings of Allah be upon him), and she came to the Messenger of Allah (peace and blessings of Allah be upon him) and said, “I have a strong, prolonged flow of blood.” He said to her: “Block it with cotton.” She said, “It is greater than that. My blood gushes.” He said, “Consider yourself to be on your menses each month for six or seven days known to Allah, then do ghusl and pray and fast for twenty-three or twenty-four days. Delay Zuhr prayer and bring ‘Asr forward, and do ghusl for them. And delay Maghrib and bring ‘Isha forward and do ghusl for them. This is the more beloved of the two ways to me.” (Narrated by Ibn Majah, al-Taharah wa Sunanuha, 619. Classed as hasan by al-Albani in Sahih Sunan Ibn Majah, no. 510). 
For more about menstruation-related issues, please see these answers: 862 , 50330 , and 1852 .
And Allah knows best.