The petition has become the most signed online petition in parliamentary history with more than 640,000 signatures.
But what is Meningitis B?
Meningitis B is a meningococcal bacterial infection and can be extremely serious as it can cause blood poisoning (septicaemia), and according to the NHS is "the leading infectious killer of babies and young children in the UK".
The Meningitis Research Foundation says that Meningitis B is "the most common cause of bacterial meningitis in the UK".
Meningitis B is an infection of the protective membranes around the brain and spinal column and can lead to severe brain damage, amputations and death. It is always treated as a medical emergency.
Meningitis B is most common in children under 1 year old, with cases peaking at 5-6 months of age.
* Severe headache
* Dislike of bright lights
* Neck stiffness
* Nausea and vomiting
* Confusion and drowsiness
* Loss of consciousness
* Fever with cold hands and feet
* Joint or muscle pain
* Rapid breathing / grunting
* Stomach cramps and diarrhoea
* Red / purple spots or bruises that do not fade under pressure
The above symptoms can appear in any order, and some may not appear at all.
Don’t wait for a rash to develop. If your child is unwell and getting worse, seek medical help immediately.
A vaccine to protect against meningitis B is available on the NHS for babies aged two months, followed by a second dose at four months and a booster at 12 months.
Parents who wish to have older children vaccinated must pay privately, although a worldwide shortage of the vaccine Bexsero means stocks are very low.
Boots has run out of supplies and CityDoc, the largest supplier of the vaccine outside of the NHS, said although existing patients would be given their boosters, there were not enough supplies to cater for new patients.
Manufacturer GlaxoSmithKline hopes to increase UK stocks by the summer.
The NHS programme is unaffected.