Note 2 - Basis of Presentation, Principles of Consolidation and Significant Accounting Policies - Schedule of Fair Value Measurements, Recurring and Nonrecurring (Details) - USD ($) $ in Thousands	12 Months Ended
Dec. 31, 2022	Dec. 31, 2021
Warrant Liability Long Term [Member]
Balance	$ 1,412	$ 8,192
Exercise of warrants		(52)
Change in fair value - net	(1,335)	(6,728)
Balance	77	1,412
Fair Value, Recurring [Member] \| Warrant Liability [Member]
Fair value of warrant liability	77	1,412
Fair Value, Recurring [Member] \| Warrant Liability [Member] \| Fair Value, Inputs, Level 1 [Member]
Fair value of warrant liability	0	0
Fair Value, Recurring [Member] \| Warrant Liability [Member] \| Fair Value, Inputs, Level 2 [Member]
Fair value of warrant liability	0	0
Fair Value, Recurring [Member] \| Warrant Liability [Member] \| Fair Value, Inputs, Level 3 [Member]
Fair value of warrant liability	$ 77	$ 1,412

Amount of gain (loss) recognized in income from liability measured at fair value on recurring basis using unobservable input (level 3).

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(1)
-URI https://asc.fasb.org/extlink&oid=126976982&loc=d3e19207-110258

+ Details

Name:	us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of settlements of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)
-URI https://asc.fasb.org/extlink&oid=126976982&loc=d3e19207-110258

+ Details

Name:	us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Fair value of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=126976982&loc=d3e19207-110258

+ Details

Name:	us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Fair value of financial and nonfinancial obligations.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=126976982&loc=d3e19207-110258

+ Details

Name:	us-gaap_LiabilitiesFairValueDisclosure
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Details

Name:	us-gaap_FairValueByLiabilityClassAxis=mbrx_WarrantLiabilityLongTermMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByMeasurementFrequencyAxis=us-gaap_FairValueMeasurementsRecurringMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByLiabilityClassAxis=mbrx_WarrantLiabilityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel1Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel2Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel3Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: