I fasted the tenth of Muharram to compensate for one of the days that I had not fasted and I was intending to fast the eleventh of Muharram as I know that it is impermissible to fast the tenth of Muharram alone. However, I had my menstruation on the eleventh of Muharram and could not fast that day. Is my fasting the tenth of Muharram alone permissible?

All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

It is permissible to fast the tenth of Muharram alone as there is no text that forbids this, although there are Hadeeths that indicate the favorability of fasting the ninth or the eleventh along with the tenth of Muharram. Ibn ‘Abbaas, said: "When the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, fasted the tenth of Muharram and commanded that it should be fasted, they (his Companions) said to him, 'O Messenger of Allaah, it is a day which the Jews and Christians glorify.’ Thereupon the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, said: 'When the next year comes, in shaa’ Allaah, we will fast the ninth (along with the tenth in order to differ from the Jews and Christians).' However, the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, died before the advent of the next year." [Muslim]

Ash-Shawkaani said, "It appears that what is more prudent is to fast three days: the ninth, the tenth and the eleventh. Thus, fasting the tenth of Muharram is of three ranks:

First one is to fast the tenth day alone,

Second is to fast the ninth and the tenth and

Third is to fast the ninth, tenth and the eleventh. This was also mentioned by Ibn Hajar.” [End of quote]

Thus, what you did is alright, especially when what prevented you from fasting the eleventh of Muharram was a Sharee‘ah-approved excuse.

Allaah Knows best.