"The link that we have with Saudi Arabia is historic, it is an important one, and it has saved the lives of potentially hundreds of people in this country,” May said in response to a question from opposition Labor Party leader Jeremy Corbyn.
Saudi Arabia and its partners launched a war on Yemen in March 2015 to reinstall its former Riyadh-allied government. The military aggression has so far killed over 13,600 Yemenis.
The war is being led by bin Salman, also Saudi Arabia’s defense minister, with the help of the US and the UK.
May’s government has remained defiant in the face of growing pressure to stop arms exports to Saudi Arabia, defending the sales amid evidence of war crimes and civilian deaths in Yemen.
The number of open licenses for weapons given to Saudi Arabia has increased considerably since Theresa May became Prime Minister, according to government figures analyzed by Sky News.
The country has been leading a coalition of nine Arab countries in airstrikes against Yemen since 2015 - and more than 10,000 people are thought to have died.
Between July 2016 and September 2017, 50 open licenses have been issued - compared with the 32 issued in the 15 months before Mrs. May entered Downing Street. This is an increase of 56%.
Open weapon sale licenses have been described as "secretive" by campaign groups because they allow an uncapped number of data-x-items to be sent to another country for five years.
There is no requirement to declare who the end user of the military data-x-items are, the license’s value cannot be provided until the end of the five-year period, and campaigners claim there is no obligation for the Government to publish the total afterwards.
The spike in deals done through open licences has coincided with a decrease in the use of standard licences, where the value of a sale is known from the outset.
A licence must be issued in order for the UK to supply weapons to a foreign body.
Although the reported sales of weapons under Mrs May are less than her predecessor David Cameron, they could be significantly higher because the value of sales through open licences during her premiership is not known.
Analysis from the Campaign Against Arms Trade (CAAT) found 257 data-x-items were traded in 2016 - rising by 175% to 707 in the first nine months of 2017.
Andrew Smith, from the Campaign Against Arms Trade, said: "By arming and supporting the Saudi regime the UK Government is complicit in the abuse of Saudi people and the terrible atrocities taking place in Yemen.
"When the Government uses open licences it makes a secretive industry even less transparent. We don't know how many arms are being sold in secret, or how much money is really being spent.
"The fact that these licences are becoming even more common is definitely a cause for concern. It is impossible for the government to stand up for human rights and democracy at the same time as it is promoting arms sales to human rights abusers and dictatorships."
The news comes on the eve of Mohammed bin Salman, Saudi Arabia's Crown Prince, visiting the UK. During the trip, he will meet Mrs May and senior members of the Royal Family.
More than a third of Britons are opposed to his visit, according to a Populus poll commissioned by CAAT - and protests are due to take place on Wednesday evening.
Human rights groups are critical of the Crown Prince for his role in the conflict in Yemen, which has plunged the country into a humanitarian crisis.
In the year before the conflict began, the number of standard licences for UK arms exports rose by a third - from 124 in 2014 to 165 in 2015. Over that period, spending by Saudi Arabia soared from £80m to £2.84bn.