Inclusion Criteria:  Subjects will be eligible if they are male or female aged between 18 to 75 years at time of consent (inclusive) with normal vital signs and a diagnosis of active mild ulcerative colitis (UC) (modified Mayo Score of 3 or 4) or moderate UC (modified Mayo Score of 5 to 8) confirmed at least 12 weeks prior to randomization by clinical and endoscopic evidence and corroborated by a histopathology report. Subjects must have an endoscopic subscore of ≥2 from and evidence of active UC extending ≥15 cm from the anal verge confirmed by a screening colonoscopy. If subjects are receiving oral or rectal 5-aminosalicylates (5-ASAs) or oral corticosteroids (≤20 mg prednisolone equivalent) for treatment of their UC, they must be on a stable dose for at least 28 days prior to randomization. Subjects who complete the Double-Blind Period of the study who, in the opinion of the Investigator, would benefit from continued treatment, may participate in the Open Label Extension (OLE) Period.  Exclusion Criteria:  Any of the following: a diagnosis of Crohn's disease, indeterminate colitis, colitis (pseudomembranous, microscopic, or ischemic) or coeliac disease, current or recent (within 12 weeks prior to randomization) evidence of fulminant colitis, proctitis (defined as a rectal inflammation within 15 cm from the anal verge), abdominal abscess, toxic megacolon, bowel obstruction, or bowel perforation; a history or evidence of any colonic resection or subtotal or total colectomy, ileostomy, colostomy, known fixed symptomatic stenosis of the intestine, unresected adenomatous colonic polyps, or colonic mucosal dysplasia. Clinically significant infections (e.g., pneumonia, pyelonephritis, or septicemia) within 4 weeks prior to randomization or previous clinically significant infections requiring hospitalization within 6 months prior to randomization, active or latent tuberculosis, infections of hepatitis B, hepatitis C, human immunodeficiency virus (HIV), or previous shingles outbreak. Active SARS-CoV-2 infection or complications related to COVID-19. A history of, or currently active, primary or secondary immunodeficiency, presence of progressive multifocal leukoencephalopathy (PML), or presence of demyelinating diseases. A history or evidence of two or more failures with biologic treatment for UC. Currently taking any medication for treatment of UC other than oral or rectal 5-ASAs (5-aminosalicylic acids) or oral corticosteroids (≤20 mg prednisolone equivalent) Been taking enemas or suppositories (other than stable dose of 5-ASA) for treatment of UC within 2 weeks prior to the Screening Visit. Been taking an unstable dose of probiotics or antidiarrheals 2 weeks prior to the Screening Visit. Had recent myocardial infarction, unstable angina, stroke, transient ischemic attack, decompensated heart failure with hospitalization, Class III/IV heart failure, Mobitz Type II 2nd degree or 3rd degree atrioventricular (AV) block, sick sinus syndrome, prolonged QT interval, Wolff Parkinson White or other conduction abnormalities, low heart rate, ongoing treatment with Class I or Class III anti-arrhythmic drugs, heart-rate-lowering calcium-channel blockers, β blockers or with any other drugs which can reduce the heart rate, have known high risk for QT/QTc prolongation, or have clinically significant abnormal findings in 12-lead ECG that the Investigator considers may jeopardize the subject's health. Forced expiratory volume in one second (FEV1) or forced expiratory vital capacity (FVC) <70% of predicted values at screening. For sites where DLCO (diffusing capacity of the lungs for carbon monoxide) will be assessed, the value (mL/min/mmHg) is < 80% of the predicted normal value for age, height, and gender. Macular oedema as assessed by OCT (Optical Coherence Tomography). History of non-response or treatment failure with MT-1303 or other sphingosine 1 phosphate (S1P) receptor modulators. Fecal microbiota transplantation (FMT) within 12 months prior to the Screening Visit.  Any of the following laboratory abnormalities:  Hemoglobin (Hb) <9.0 g/dL. White blood cell (WBC) count <3.50 × 109/L (<3,500/µL). Neutrophil count <1.50 × 109/L (<1,500/µL). Lymphocyte count <0.80 × 109/L (<800/µL). Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) >2 × the upper limit of normal (ULN). Bilirubin >1.5 x the ULN; subjects with Gilbert's syndrome may be enrolled with total bilirubin up to 5.0 mg/dl. Positive stool tests for enteric pathogens, pathogenic ova or parasites, or Clostridium difficile (C. difficile) during the Screening Period. If subject has a history of recent C. difficile infection (within 60 days prior to Screening Visit), they should not be considered for study enrollment until subject has been treated for C. difficile and is symptom free for at least 14 days prior to the Screening Visit. Any physical or mental conditions which would interfere with the study participation, collection of data, or study completion as determined by the Investigator.