Praise be to Allah.
The Muslim is always commanded to avoid najaasah (impure things), because Allaah says (interpretation of the meaning):
“And purify your garments!”
Menstrual blood is naajis (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 Allaah be upon him), the women used to wear special clothes at the time of menstruation, because it was narrated that Umm Salamah (may Allaah 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-Bukhaari, al-Hayd, 311). And the general guideline is that things are permitted, and there is no evidence to indicate that this is not allowed. So it is not correct to say that this is not allowed. In fact there are reports which indicate that it is permitted to use cotton to check the flow of blood.
It was narrated from Hamnah bint Jahsh that she menstruated at the time of the Messenger of Allaah (peace and blessings of Allaah be upon him), and she came to the Messenger of Allaah (peace and blessings of Allaah 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 Allaah, 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 ‘Ishaa’ forward and do ghusl for them. This is the more beloved of the two ways to me.” (Narrated by Ibn Maajah, al-Tahaarah wa Sunanuhaa, 619. Classed as hasan by al-Albaani in Saheeh Sunan Ibn Maajah, no. 510).
And Allaah knows best.