Can he put out his arm to stop a woman from passing in front of him whilst he is praying?

Praise
be to Allah

What is prescribed is for the worshipper to stop the person
who wants to pass in front of him, because of the report narrated by al-Bukhaari
(509) and Muslim (505) from Abu Sa‘eed al-Khudri (may Allah be pleased with
him) who said: I heard the Prophet (blessings and peace of Allah be upon
him) say: “If one of you prays facing towards something that is screening
him from the people, and someone wants to pass in front of him, let him push
him, and if he insists then let him fight him, for he is a devil.” 

This hadith is general in meaning and refers to preventing
both men and women from passing in front of one. In fact preventing a woman
from doing so is more appropriate, because her passing in front of the
worshipper interrupts the prayer, because of what is proven from the hadith
of Abu Hurayrah (may Allah be pleased with him) who said: The Messenger of
Allah (blessings and peace of Allah be upon him) said: “Prayer is
interrupted by a woman, a donkey and a dog, but something like the back of a
saddle protects against that.” 

In most cases, objecting with a gesture of the hand alerts
the one who wants to pass, without needing to touch the person. 

If it so happens that one touches the person, it is touching
with a barrier, for a need, so it is permissible, so long as there is no
risk of fitnah. 

He may also pre-empt her by stepping forwards towards the
sutrah so that she will have to pass behind him. Ibn Khuzaymah (82 7)
narrated from Ibn ‘Abbaas that the Prophet (blessings and peace of Allah be
upon him) was praying, when a sheep wanted to pass in front of him, so he
stepped towards the qiblah before it could pass in front of him, until his
stomach was touching the wall that was in the direction of the qiblah. 

Classed as saheeh by al-Albaani in Sifat as-Salaah (p.
83) 

If it is possible to alert the woman in question by gesturing
towards her with his hand or by saying tasbeeh, if she does not understand
his gesture, then pointing at her so as to prevent her from passing in front
of him – if he does that, it is good and will fulfil the purpose, without
having to touch her or push her or be exposed to fitnah in his prayer.

Ash-Sharnabilaali (may Allah have mercy on him) said: 

A concession is granted allowing the worshipper to ward off
the one who wants to pass in front of him by means of a gesture, with a tilt
of the head or a blink of the eye and so on, as the Prophet (blessings and
peace of Allah be upon him) did with the two sons of Umm Salamah. Or he may
ward him off by saying tasbeeh, because the Prophet (blessings and peace of
Allah be upon him) said: If something bothers one of you when he is praying,
let him say tasbeeh, but it is makrooh to combine both, i.e., to combine
gesturing with saying tasbeeh, because one of them should suffice. A man may
ward him off by raising his voice in recitation, even if it is louder than
when he usually recites out loud. A woman may ward off (someone who wants to
pass in front of her) by gesturing or clapping her hands (by striking the
palm of the left hand with the back of the right hand), because women may
clap, but a woman should not raise her voice in recitation or saying tasbeeh,
because that is fitnah, so a woman is not required to use it in order to
ward off someone who wants to pass in front of her when she is praying.

End quote from Maraaqi al-Falaah Sharh Noor al-Eedaah
(367) 

In al-Muheet al-Burhaani fi’l-Fiqh an-Nu‘maani (1/429)
it says: 

Chapter nineteen: passing in front of a worshipper who is
praying, and the worshipper warding off the one who wants to pass in front
of him; using a sutrah (screen) and issues concerning that. 

Muhammad (may Allah have mercy on him) said in al-Jaami‘
as-Sagheer, concerning a woman who wants to pass in front of a man when
he is praying: He should stop her…. End quote. 

For more information, please see the answers to questions no.
118153 and 96912. 

And Allah knows best.